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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000668
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
=> [2]
=> 2
([],2)
=> [2,2]
=> 2
([(0,1)],2)
=> [3]
=> 3
([],3)
=> [2,2,2,2]
=> 2
([(1,2)],3)
=> [6]
=> 6
([(0,1),(0,2)],3)
=> [3,2]
=> 6
([(0,2),(2,1)],3)
=> [4]
=> 4
([(0,2),(1,2)],3)
=> [3,2]
=> 6
([(2,3)],4)
=> [6,6]
=> 6
([(1,2),(1,3)],4)
=> [6,2,2]
=> 6
([(0,1),(0,2),(0,3)],4)
=> [3,2,2,2]
=> 6
([(0,2),(0,3),(3,1)],4)
=> [7]
=> 7
([(0,1),(0,2),(1,3),(2,3)],4)
=> [4,2]
=> 4
([(1,2),(2,3)],4)
=> [4,4]
=> 4
([(0,3),(3,1),(3,2)],4)
=> [4,2]
=> 4
([(1,3),(2,3)],4)
=> [6,2,2]
=> 6
([(0,3),(1,3),(3,2)],4)
=> [4,2]
=> 4
([(0,3),(1,3),(2,3)],4)
=> [3,2,2,2]
=> 6
([(0,3),(1,2)],4)
=> [3,3,3]
=> 3
([(0,3),(1,2),(1,3)],4)
=> [5,3]
=> 15
([(0,2),(0,3),(1,2),(1,3)],4)
=> [3,2,2]
=> 6
([(0,3),(2,1),(3,2)],4)
=> [5]
=> 5
([(0,3),(1,2),(2,3)],4)
=> [7]
=> 7
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [7,2,2]
=> 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [4,2,2,2]
=> 4
([(0,3),(0,4),(4,1),(4,2)],5)
=> [7,2,2]
=> 14
([(1,2),(1,3),(2,4),(3,4)],5)
=> [4,4,2,2]
=> 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [5,2]
=> 10
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,3,3]
=> 12
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [5,4]
=> 20
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [4,2,2]
=> 4
([(1,4),(4,2),(4,3)],5)
=> [4,4,2,2]
=> 4
([(0,4),(4,1),(4,2),(4,3)],5)
=> [4,2,2,2]
=> 4
([(1,4),(2,4),(4,3)],5)
=> [4,4,2,2]
=> 4
([(0,4),(1,4),(4,2),(4,3)],5)
=> [4,2,2]
=> 4
([(0,4),(1,4),(2,4),(4,3)],5)
=> [4,2,2,2]
=> 4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [5,3,2,2]
=> 30
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [3,2,2,2,2]
=> 6
([(0,4),(1,4),(2,3),(4,2)],5)
=> [5,2]
=> 10
([(0,4),(1,3),(2,3),(3,4)],5)
=> [7,2,2]
=> 14
([(0,4),(1,2),(1,4),(2,3)],5)
=> [8,3]
=> 24
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [5,4]
=> 20
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [7,2]
=> 14
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [4,2,2]
=> 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> [10]
=> 10
([(0,2),(0,4),(3,1),(4,3)],5)
=> [5,4]
=> 20
([(0,4),(1,2),(1,3),(3,4)],5)
=> [10,2]
=> 10
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [8]
=> 8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [7,2,2]
=> 14
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [5,3,2,2]
=> 30
Description
The least common multiple of the parts of the partition.
Matching statistic: St001782
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(load all 2 compositions to match this statistic)
Values
([],1)
=> 2
([],2)
=> 2
([(0,1)],2)
=> 3
([],3)
=> 2
([(1,2)],3)
=> 6
([(0,1),(0,2)],3)
=> 6
([(0,2),(2,1)],3)
=> 4
([(0,2),(1,2)],3)
=> 6
([(2,3)],4)
=> 6
([(1,2),(1,3)],4)
=> 6
([(0,1),(0,2),(0,3)],4)
=> 6
([(0,2),(0,3),(3,1)],4)
=> 7
([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(1,2),(2,3)],4)
=> 4
([(0,3),(3,1),(3,2)],4)
=> 4
([(1,3),(2,3)],4)
=> 6
([(0,3),(1,3),(3,2)],4)
=> 4
([(0,3),(1,3),(2,3)],4)
=> 6
([(0,3),(1,2)],4)
=> 3
([(0,3),(1,2),(1,3)],4)
=> 15
([(0,2),(0,3),(1,2),(1,3)],4)
=> 6
([(0,3),(2,1),(3,2)],4)
=> 5
([(0,3),(1,2),(2,3)],4)
=> 7
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 14
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 4
([(0,3),(0,4),(4,1),(4,2)],5)
=> 14
([(1,2),(1,3),(2,4),(3,4)],5)
=> 4
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 10
([(0,3),(0,4),(3,2),(4,1)],5)
=> 12
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 20
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
([(1,4),(4,2),(4,3)],5)
=> 4
([(0,4),(4,1),(4,2),(4,3)],5)
=> 4
([(1,4),(2,4),(4,3)],5)
=> 4
([(0,4),(1,4),(4,2),(4,3)],5)
=> 4
([(0,4),(1,4),(2,4),(4,3)],5)
=> 4
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 30
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 6
([(0,4),(1,4),(2,3),(4,2)],5)
=> 10
([(0,4),(1,3),(2,3),(3,4)],5)
=> 14
([(0,4),(1,2),(1,4),(2,3)],5)
=> 24
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 20
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> 14
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 4
([(0,4),(1,2),(1,4),(4,3)],5)
=> 10
([(0,2),(0,4),(3,1),(4,3)],5)
=> 20
([(0,4),(1,2),(1,3),(3,4)],5)
=> 10
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 8
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 14
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> 30
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)
=> ? = 6
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> ? = 10
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> ? = 30
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
=> ? = 12
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)
=> ? = 28
([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)
=> ? = 12
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> ? = 14
([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)
=> ? = 18
([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)
=> ? = 12
([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)
=> ? = 18
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)
=> ? = 6
([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)
=> ? = 12
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)
=> ? = 18
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
=> ? = 12
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
=> ? = 6
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> ? = 8
([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7)
=> ? = 12
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> ? = 30
([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)
=> ? = 12
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)
=> ? = 18
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
=> ? = 6
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
=> ? = 6
([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)
=> ? = 12
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)
=> ? = 6
([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)
=> ? = 6
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> ? = 10
([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)
=> ? = 12
([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)
=> ? = 12
([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)
=> ? = 10
([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
=> ? = 30
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
=> ? = 12
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> ? = 10
([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)
=> ? = 12
([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
=> ? = 12
([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)
=> ? = 18
([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ? = 12
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)
=> ? = 18
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
=> ? = 6
([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)
=> ? = 30
([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)
=> ? = 18
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
=> ? = 14
([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)
=> ? = 28
([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)
=> ? = 12
([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7)
=> ? = 12
([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)
=> ? = 12
([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)
=> ? = 6
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
=> ? = 10
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 8
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 10
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> ? = 10
Description
The order of rowmotion on the set of order ideals of a poset.
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