Your data matches 80 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001605
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00202: Integer partitions first row removalInteger partitions
Mp00313: Integer partitions Glaisher-Franklin inverseInteger partitions
St001605: 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]
=> [2,1]
=> 1
([],5)
=> [1,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([],6)
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> [2,2,1]
=> 6
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,1,1,1]
=> [2,2]
=> 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 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]
=> [2,1]
=> 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,1,1]
=> [2,1]
=> 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [2,1]
=> [1,1,1]
=> 2
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition. Two colourings are considered equal, if they are obtained by an action of the cyclic group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001232
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00230: Integer partitions parallelogram polyominoDyck paths
Mp00222: Dyck paths peaks-to-valleysDyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 11%distinct values known / distinct values provided: 2%
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
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? = 2 + 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]
=> ? = 6 + 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
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 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
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 2
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? = 2 + 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: St001804
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00033: Dyck paths to two-row standard tableauStandard tableaux
St001804: Standard tableaux ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [[1,3,4,5,6],[2,7,8,9,10]]
=> ? = 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [[1,3,4,5,6,7],[2,8,9,10,11,12]]
=> ? = 2
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [[1,3,4,5,7],[2,6,8,9,10]]
=> ? = 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [[1,3,5,6],[2,4,7,8]]
=> 2
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]]
=> ? = 6
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [[1,3,4,5,6,8],[2,7,9,10,11,12]]
=> ? = 2
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [[1,3,4,5,8],[2,6,7,9,10]]
=> ? = 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [[1,3,4,6,7],[2,5,8,9,10]]
=> ? = 3
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [[1,3,5,7],[2,4,6,8]]
=> 2
Description
The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. A cylindrical tableau associated with a standard Young tableau $T$ is the skew row-strict tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle. This statistic equals $\max_C\big(\ell(C) - \ell(T)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
Matching statistic: St001195
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00199: Dyck paths prime Dyck pathDyck paths
St001195: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 1 = 2 - 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 - 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 - 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1 = 2 - 1
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St001207
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00025: Dyck paths to 132-avoiding permutationPermutations
St001207: Permutations ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ? = 1 + 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => ? = 2 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [3,4,2,1] => 3 = 2 + 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 6 + 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ? = 1 + 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ? = 3 + 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [4,3,2,1] => 3 = 2 + 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St001208
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00201: Dyck paths RingelPermutations
St001208: Permutations ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 1 - 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,1,4,5,6,7,2] => ? = 2 - 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => ? = 1 - 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 1 = 2 - 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [3,1,4,5,6,7,8,2] => ? = 6 - 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [7,1,4,5,6,2,3] => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => ? = 1 - 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => ? = 3 - 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 1 = 2 - 1
Description
The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$.
Matching statistic: St001314
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00199: Dyck paths prime Dyck pathDyck paths
St001314: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 + 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
Description
The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra.
Matching statistic: St001514
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00199: Dyck paths prime Dyck pathDyck paths
St001514: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 + 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
Description
The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule.
Matching statistic: St001526
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00199: Dyck paths prime Dyck pathDyck paths
St001526: Dyck paths ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3 = 2 + 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 + 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 1 + 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 3 + 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 3 = 2 + 1
Description
The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001582
Mp00110: Posets Greene-Kleitman invariantInteger partitions
Mp00043: Integer partitions to Dyck pathDyck paths
Mp00129: Dyck paths to 321-avoiding permutation (Billey-Jockusch-Stanley)Permutations
St001582: Permutations ⟶ ℤResult quality: 2% values known / values provided: 5%distinct values known / distinct values provided: 2%
Values
([],4)
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => ? = 1 + 1
([],5)
=> [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => ? = 2 + 1
([(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(2,3),(2,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(1,2),(1,3),(1,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => ? = 1 + 1
([(0,4),(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,4),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(1,4),(2,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,4),(1,2),(1,3)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [2,3,1,4] => 3 = 2 + 1
([],6)
=> [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,1,3,4,5,6,7] => ? = 6 + 1
([(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(3,4),(3,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(2,3),(2,4),(2,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,4),(1,5),(4,3),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(2,3),(3,4),(3,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(1,5),(2,5),(3,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
=> [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => ? = 1 + 1
([(0,5),(1,5),(2,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => ? = 3 + 1
([(0,5),(1,5),(2,3),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
([(1,5),(2,3),(2,5),(3,4)],6)
=> [3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [2,3,4,1] => 3 = 2 + 1
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
The following 70 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000508Eigenvalues of the random-to-random operator acting on a simple module. St000735The last entry on the main diagonal of a standard tableau. St000744The length of the path to the largest entry in a standard Young tableau. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001413Half the length of the longest even length palindromic prefix of a binary word. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001556The number of inversions of the third entry of a permutation. St001557The number of inversions of the second entry of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000044The number of vertices of the unicellular map given by a perfect matching. St000017The number of inversions of a standard tableau. St001721The degree of a binary word. St000016The number of attacking pairs of a standard tableau. St000958The number of Bruhat factorizations of a permutation. St001651The Frankl number of a lattice. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001501The dominant dimension of magnitude 1 Nakayama algebras. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. 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. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001172The number of 1-rises at odd height of a Dyck path. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001732The number of peaks visible from the left. St000661The number of rises of length 3 of a Dyck path. St000674The number of hills of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001498The normalised height of a Nakayama algebra with magnitude 1. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000981The length of the longest zigzag subpath. St001471The magnitude of a Dyck path. St000024The number of double up and double down steps of a Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St000395The sum of the heights of the peaks of a Dyck path. St000331The number of upper interactions of a Dyck path. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St000144The pyramid weight of the Dyck path.