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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001782
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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
([],4)
=> 2
([(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
([],5)
=> 2
([(3,4)],5)
=> 6
([(2,3),(2,4)],5)
=> 6
([(1,2),(1,3),(1,4)],5)
=> 6
([(0,1),(0,2),(0,3),(0,4)],5)
=> 6
([(0,2),(0,3),(0,4),(4,1)],5)
=> 42
([(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
([(1,3),(1,4),(4,2)],5)
=> 14
([(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
([(2,3),(3,4)],5)
=> 4
([(1,4),(4,2),(4,3)],5)
=> 4
([(0,4),(4,1),(4,2),(4,3)],5)
=> 4
([(2,4),(3,4)],5)
=> 6
([(1,4),(2,4),(4,3)],5)
=> 4
([(0,4),(1,4),(4,2),(4,3)],5)
=> 4
([(1,4),(2,4),(3,4)],5)
=> 6
([(0,4),(1,4),(2,4),(4,3)],5)
=> 4
([(0,4),(1,4),(2,4),(3,4)],5)
=> 6
([(0,4),(1,4),(2,3)],5)
=> 6
([(0,4),(1,3),(2,3),(2,4)],5)
=> 24
Description
The order of rowmotion on the set of order ideals of a poset.
Matching statistic: St000668
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 26%
St000668: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 26%
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
([],4)
=> [2,2,2,2,2,2,2,2]
=> ? = 2
([(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
([],5)
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 2
([(3,4)],5)
=> [6,6,6,6]
=> ? = 6
([(2,3),(2,4)],5)
=> [6,6,2,2,2,2]
=> ? = 6
([(1,2),(1,3),(1,4)],5)
=> [6,2,2,2,2,2,2]
=> ? = 6
([(0,1),(0,2),(0,3),(0,4)],5)
=> [3,2,2,2,2,2,2,2]
=> ? = 6
([(0,2),(0,3),(0,4),(4,1)],5)
=> [7,6]
=> ? = 42
([(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
([(1,3),(1,4),(4,2)],5)
=> [14]
=> ? = 14
([(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
([(2,3),(3,4)],5)
=> [4,4,4,4]
=> ? = 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
([(2,4),(3,4)],5)
=> [6,6,2,2,2,2]
=> ? = 6
([(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
([(1,4),(2,4),(3,4)],5)
=> [6,2,2,2,2,2,2]
=> ? = 6
([(0,4),(1,4),(2,4),(4,3)],5)
=> [4,2,2,2]
=> 4
([(0,4),(1,4),(2,4),(3,4)],5)
=> [3,2,2,2,2,2,2,2]
=> ? = 6
([(0,4),(1,4),(2,3)],5)
=> [6,3,3,3]
=> ? = 6
([(0,4),(1,3),(2,3),(2,4)],5)
=> [8,3,2]
=> ? = 24
([(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),(1,4),(2,3),(2,4)],5)
=> [6,5,3]
=> ? = 30
([(0,4),(1,4),(2,3),(3,4)],5)
=> [7,6]
=> ? = 42
([(1,4),(2,3)],5)
=> [6,6,6]
=> ? = 6
([(1,4),(2,3),(2,4)],5)
=> [10,6]
=> ? = 30
([(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
([(1,3),(1,4),(2,3),(2,4)],5)
=> [6,2,2,2,2]
=> ? = 6
([(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
([(0,4),(1,2),(1,3)],5)
=> [6,3,3,3]
=> ? = 6
([(0,4),(1,2),(1,3),(1,4)],5)
=> [6,5,3]
=> ? = 30
([(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),(1,4)],5)
=> [8,3,2]
=> ? = 24
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [5,3,2,2]
=> 30
([(1,4),(2,3),(3,4)],5)
=> [14]
=> ? = 14
([],6)
=> [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 2
([(4,5)],6)
=> [6,6,6,6,6,6,6,6]
=> ? = 6
([(3,4),(3,5)],6)
=> [6,6,6,6,2,2,2,2,2,2,2,2]
=> ? = 6
([(2,3),(2,4),(2,5)],6)
=> [6,6,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 6
([(1,2),(1,3),(1,4),(1,5)],6)
=> [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 6
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
=> ? = 6
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> [7,6,6,6]
=> ? = 42
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> [7,6,2,2,2,2]
=> ? = 42
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
=> [7,2,2,2,2,2,2]
=> ? = 14
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> [4,2,2,2,2,2,2,2]
=> ? = 4
([(1,3),(1,4),(1,5),(5,2)],6)
=> [14,6,6]
=> ? = 42
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
=> [7,6,2,2,2,2]
=> ? = 42
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> [14,2,2,2,2]
=> ? = 14
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [4,4,2,2,2,2,2,2]
=> ? = 4
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
=> [6,4,3,3]
=> ? = 12
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
=> [8,4,2]
=> ? = 8
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [5,4,2,2]
=> ? = 20
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)
=> [6,5,4]
=> ? = 60
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,4,2,2]
=> ? = 20
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
=> [7,6,6]
=> ? = 42
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> [10,7]
=> ? = 70
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [7,2,2,2,2]
=> ? = 14
([(2,3),(2,4),(4,5)],6)
=> [14,14]
=> ? = 14
([(1,4),(1,5),(5,2),(5,3)],6)
=> [14,2,2,2,2]
=> ? = 14
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
=> [7,2,2,2,2,2,2]
=> ? = 14
([(2,3),(2,4),(3,5),(4,5)],6)
=> [4,4,4,4,2,2,2,2]
=> ? = 4
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [10,2,2]
=> ? = 10
Description
The least common multiple of the parts of the partition.
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