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Your data matches 76 different statistics following compositions of up to 3 maps.
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Matching statistic: St000681
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000681: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],4)
=> [1,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,1,1]
=> 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [1,1,1]
=> 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [1,1]
=> 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [2,1,1]
=> [1,1]
=> 1
Description
The Grundy value of Chomp on Ferrers diagrams.
Players take turns and choose a cell of the diagram, cutting off all cells below and to the right of this cell in English notation. The player who is left with the single cell partition looses. The traditional version is played on chocolate bars, see [1].
This statistic is the Grundy value of the partition, that is, the smallest non-negative integer which does not occur as value of a partition obtained by a single move.
Matching statistic: St000689
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000689: Dyck paths ⟶ ℤResult quality: 29% ●values known / values provided: 34%●distinct values known / distinct values provided: 29%
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000689: Dyck paths ⟶ ℤResult quality: 29% ●values known / values provided: 34%●distinct values known / distinct values provided: 29%
Values
([],4)
=> [1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 2
([(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(2,5),(2,6),(5,4),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 1
Description
The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid.
The correspondence between LNakayama algebras and Dyck paths is explained in [[St000684]]. A module $M$ is $n$-rigid, if $\operatorname{Ext}^i(M,M)=0$ for $1\leq i\leq n$.
This statistic gives the maximal $n$ such that the minimal generator-cogenerator module $A \oplus D(A)$ of the LNakayama algebra $A$ corresponding to a Dyck path is $n$-rigid.
An application is to check for maximal $n$-orthogonal objects in the module category in the sense of [2].
Matching statistic: St001200
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 29% ●values known / values provided: 34%●distinct values known / distinct values provided: 29%
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 29% ●values known / values provided: 34%●distinct values known / distinct values provided: 29%
Values
([],4)
=> [1,1,1,1]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 3 = 1 + 2
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4 = 2 + 2
([(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 3 = 1 + 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 3 + 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,5),(2,6),(5,4),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,1,1]
=> [3,3,1]
=> [1,1,1,0,1,0,0,1,0,0]
=> 3 = 1 + 2
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001514
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001514: Dyck paths ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 43%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001514: Dyck paths ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 43%
Values
([],4)
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3 = 1 + 2
([],5)
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4 = 2 + 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3 = 1 + 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 3 + 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,4),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,2),(1,3),(1,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,2),(1,3)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 3 = 1 + 2
([(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 1 + 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,5),(1,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 3 = 1 + 2
([],7)
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 4 + 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(4,5),(4,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(3,4),(3,5),(3,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(2,3),(2,4),(2,5),(2,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
=> [2,1,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3 + 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=> ? = 2 + 2
Description
The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule.
Matching statistic: St000528
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 57%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 57%
Values
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4 = 1 + 3
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 2 + 3
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4 = 1 + 3
([],6)
=> [1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 3 + 3
([(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 5 = 2 + 3
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 4 = 1 + 3
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 4 = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7)
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? = 1 + 3
([(2,5),(2,6),(5,4),(6,3)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 3
Description
The height of a poset.
This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 20%●distinct values known / distinct values provided: 14%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 14% ●values known / values provided: 20%●distinct values known / distinct values provided: 14%
Values
([],4)
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? = 1 + 2
([],5)
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 3 + 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(2,3)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,4),(1,5),(2,3),(2,5)],6)
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,3),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3 = 1 + 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000264
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Values
([],4)
=> ([],4)
=> [4] => ([],4)
=> ? = 1 + 2
([],5)
=> ([],5)
=> [5] => ([],5)
=> ? = 2 + 2
([(3,4)],5)
=> ([(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(2,3),(2,4)],5)
=> ([(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(2,4),(3,4)],5)
=> ([(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> ([(1,4),(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
([],6)
=> ([],6)
=> [6] => ([],6)
=> ? = 3 + 2
([(4,5)],6)
=> ([(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(3,4),(3,5)],6)
=> ([(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> ([(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(3,4),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(3,5),(4,5)],6)
=> ([(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> ([(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> ([(0,1),(2,5),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> ([(1,2),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(1,5),(2,4),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> ([(1,5),(2,5),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> ([(0,5),(1,5),(2,4),(3,4)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)
=> ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7)
=> ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
=> ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7)
=> ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)
=> ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)
=> ([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)
=> ([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)
=> ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)
=> ([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7)
=> ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7)
=> ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
([(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7)
=> ([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)
=> [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 3 = 1 + 2
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St001912
Values
([],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(3,4)],5)
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,4),(3,4)],5)
=> ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [6]
=> 3
([(4,5)],6)
=> ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(2,3),(2,4),(2,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,3),(2,4),(4,5)],6)
=> ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(3,4),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,3),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(3,5),(4,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(2,5),(3,5),(5,4)],6)
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [5]
=> 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,5),(3,4)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [4]
=> 1
([],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 4
([(5,6)],7)
=> ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(4,5),(4,6)],7)
=> ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(3,4),(3,5),(3,6)],7)
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(2,3),(2,4),(2,5),(2,6)],7)
=> ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
=> ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
=> ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 3
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
=> ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
=> ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
=> ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
=> ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> ([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
=> ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> ([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> ([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> ([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> ([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> ([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
=> ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(2,4),(2,5),(2,6),(6,3)],7)
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
=> ([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 2
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> ([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 1
Description
The length of the preperiod in Bulgarian solitaire corresponding to an integer partition.
Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row.
Matching statistic: St000080
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Values
([],4)
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 1 + 2
([],5)
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 2 + 2
([(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> 3 = 1 + 2
([],6)
=> [1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5 = 3 + 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
=> 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> 3 = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> 3 = 1 + 2
([],7)
=> [1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1],[]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 4 + 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(4,5),(4,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(3,4),(3,5),(3,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(2,3),(2,4),(2,5),(2,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
=> [2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
=> ? = 3 + 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(2,4),(2,5),(2,6),(6,3)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ? = 2 + 2
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? = 1 + 2
Description
The rank of the poset.
Matching statistic: St000864
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000864: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000864: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Values
([],4)
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => 3 = 1 + 2
([],5)
=> [1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => 4 = 2 + 2
([(3,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [4,3,2,1,5] => 3 = 1 + 2
([],6)
=> [1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1] => 5 = 3 + 2
([(4,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [[1,6],[2],[3],[4],[5]]
=> [5,4,3,2,1,6] => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [[1,5,6],[2],[3],[4]]
=> [4,3,2,1,5,6] => 3 = 1 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [5,3,2,6,1,4] => 3 = 1 + 2
([],7)
=> [1,1,1,1,1,1,1]
=> [[1],[2],[3],[4],[5],[6],[7]]
=> [7,6,5,4,3,2,1] => ? = 4 + 2
([(5,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(4,5),(4,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(3,4),(3,5),(3,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(2,3),(2,4),(2,5),(2,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
=> [2,1,1,1,1,1]
=> [[1,7],[2],[3],[4],[5],[6]]
=> [6,5,4,3,2,1,7] => ? = 3 + 2
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(2,4),(2,5),(2,6),(6,3)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [3,1,1,1,1]
=> [[1,6,7],[2],[3],[4],[5]]
=> [5,4,3,2,1,6,7] => ? = 2 + 2
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
=> [4,1,1,1]
=> [[1,5,6,7],[2],[3],[4]]
=> [4,3,2,1,5,6,7] => ? = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [5,3,2,6,1,4,7] => ? = 1 + 2
Description
The number of circled entries of the shifted recording tableau of a permutation.
The diagram of a strict partition $\lambda_1 < \lambda_2 < \dots < \lambda_\ell$ of $n$ is a tableau with $\ell$ rows, the $i$-th row being indented by $i$ cells. A shifted standard Young tableau is a filling of such a diagram, where entries in rows and columns are strictly increasing.
The shifted Robinson-Schensted algorithm [1] associates to a permutation a pair $(P, Q)$ of standard shifted Young tableaux of the same shape, where off-diagonal entries in $Q$ may be circled.
This statistic records the number of circled entries in $Q$.
The following 66 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000863The length of the first row of the shifted shape of a permutation. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001286The annihilation number of a graph. St001703The villainy of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001331The size of the minimal feedback vertex set. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001593This is the number of standard Young tableaux of the given shifted shape. St001060The distinguishing index of a graph. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001309The number of four-cliques in a graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001793The difference between the clique number and the chromatic number of a graph. St000387The matching number of a graph. St000759The smallest missing part in an integer partition. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St000172The Grundy number of a graph. St001112The 3-weak dynamic number of a graph. St000439The position of the first down step of a Dyck path. St000785The number of distinct colouring schemes of a graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000323The minimal crossing number of a graph. St000370The genus of a graph. St000552The number of cut vertices of a graph. St001826The maximal number of leaves on a vertex of a graph. St001957The number of Hasse diagrams with a given underlying undirected graph. St000422The energy of a graph, if it is integral. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St000655The length of the minimal rise of a Dyck path. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000632The jump number of the poset. St001307The number of induced stars on four vertices in a graph. St001479The number of bridges of a graph. St000660The number of rises of length at least 3 of a Dyck path. St000475The number of parts equal to 1 in a partition. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000929The constant term of the character polynomial of an integer partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000322The skewness of a graph. St001545The second Elser number of a connected graph. St000260The radius of a connected graph. St000659The number of rises of length at least 2 of a Dyck path. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St000617The number of global maxima of a Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000142The number of even parts of a partition. St001092The number of distinct even parts of a partition. St001252Half the sum of the even parts of a partition. St001330The hat guessing number of a graph. St001484The number of singletons of an integer partition. St001645The pebbling number of a connected graph. St000678The number of up steps after the last double rise of a Dyck path.
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