Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000848
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Mapping
St000848: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => 1
([(0,1)],2)
 => 0
([],3)
 => 3
([(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => 1
([(0,2),(2,1)],3)
 => 0
([(0,2),(1,2)],3)
 => 1
([],4)
 => 12
([(2,3)],4)
 => 6
([(1,2),(1,3)],4)
 => 4
([(0,1),(0,2),(0,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => 2
([(0,3),(3,1),(3,2)],4)
 => 1
([(1,3),(2,3)],4)
 => 4
([(0,3),(1,3),(3,2)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 3
([(0,3),(1,2),(1,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
([(0,3),(2,1),(3,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 1
([],5)
 => 60
([(3,4)],5)
 => 30
([(2,3),(2,4)],5)
 => 20
([(1,2),(1,3),(1,4)],5)
 => 15
([(0,1),(0,2),(0,3),(0,4)],5)
 => 12
([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 4
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
([(1,3),(1,4),(4,2)],5)
 => 7
([(0,3),(0,4),(4,1),(4,2)],5)
 => 4
([(1,2),(1,3),(2,4),(3,4)],5)
 => 5
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => 3
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(2,3),(3,4)],5)
 => 10
([(1,4),(4,2),(4,3)],5)
 => 5
([(0,4),(4,1),(4,2),(4,3)],5)
 => 3
([(2,4),(3,4)],5)
 => 20
([(1,4),(2,4),(4,3)],5)
 => 5
([(0,4),(1,4),(4,2),(4,3)],5)
 => 2
([(1,4),(2,4),(3,4)],5)
 => 15
([(0,4),(1,4),(2,4),(4,3)],5)
 => 3
([(0,4),(1,4),(2,4),(3,4)],5)
 => 12
([(0,4),(1,4),(2,3)],5)
 => 10
([(0,4),(1,3),(2,3),(2,4)],5)
 => 8
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 7
Description
The balance constant multiplied with the number of linear extensions of a poset. A pair of elements $x,y$ of a poset is $\alpha$-balanced if the proportion $P(x,y)$ of linear extensions where $x$ comes before $y$ is between $\alpha$ and $1-\alpha$. The balance constant of a poset is $\max\min(P(x,y), P(y,x)).$ Kislitsyn [1] conjectured that every poset which is not a chain is $1/3$-balanced. Brightwell, Felsner and Trotter [2] show that it is at least $(1-\sqrt 5)/10$-balanced. Olson and Sagan [3] exhibit various posets that are $1/2$-balanced.