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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001909

St001909: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

([],1)
 => 2
([],2)
 => 4
([(0,1)],2)
 => 4
([],3)
 => 8
([(1,2)],3)
 => 8
([(0,1),(0,2)],3)
 => 8
([(0,2),(2,1)],3)
 => 7
([(0,2),(1,2)],3)
 => 8
([],4)
 => 16
([(2,3)],4)
 => 16
([(1,2),(1,3)],4)
 => 16
([(0,1),(0,2),(0,3)],4)
 => 16
([(0,2),(0,3),(3,1)],4)
 => 14
([(0,1),(0,2),(1,3),(2,3)],4)
 => 13
([(1,2),(2,3)],4)
 => 14
([(0,3),(3,1),(3,2)],4)
 => 13
([(1,3),(2,3)],4)
 => 16
([(0,3),(1,3),(3,2)],4)
 => 13
([(0,3),(1,3),(2,3)],4)
 => 16
([(0,3),(1,2)],4)
 => 16
([(0,3),(1,2),(1,3)],4)
 => 16
([(0,2),(0,3),(1,2),(1,3)],4)
 => 16
([(0,3),(2,1),(3,2)],4)
 => 11
([(0,3),(1,2),(2,3)],4)
 => 14
([],5)
 => 32
([(3,4)],5)
 => 32
([(2,3),(2,4)],5)
 => 32
([(1,2),(1,3),(1,4)],5)
 => 32
([(0,1),(0,2),(0,3),(0,4)],5)
 => 32
([(0,2),(0,3),(0,4),(4,1)],5)
 => 28
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 26
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 25
([(1,3),(1,4),(4,2)],5)
 => 28
([(0,3),(0,4),(4,1),(4,2)],5)
 => 26
([(1,2),(1,3),(2,4),(3,4)],5)
 => 26
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 19
([(0,3),(0,4),(3,2),(4,1)],5)
 => 25
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 24
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 23
([(2,3),(3,4)],5)
 => 28
([(1,4),(4,2),(4,3)],5)
 => 26
([(0,4),(4,1),(4,2),(4,3)],5)
 => 25
([(2,4),(3,4)],5)
 => 32
([(1,4),(2,4),(4,3)],5)
 => 26
([(0,4),(1,4),(4,2),(4,3)],5)
 => 23
([(1,4),(2,4),(3,4)],5)
 => 32
([(0,4),(1,4),(2,4),(4,3)],5)
 => 25
([(0,4),(1,4),(2,4),(3,4)],5)
 => 32
([(0,4),(1,4),(2,3)],5)
 => 32
([(0,4),(1,3),(2,3),(2,4)],5)
 => 32

Description

The number of interval-closed sets of a poset. For a poset

$P$ and a subset

$I$ of

$P$ , we say that

$I$ is an ''interval-closed'' set if for all

$x, y \in I$ such that

$x \leq y$ , then

$z \in I$ if

$x \leq z \leq y$ . There is a bijection between interval-closed sets of a poset

$P$ and pairs of disjoint antichains

$(A, B)$ of

$P$ such that any element in

$B$ is in the order ideal

$\Delta(A)$ generated by

$A$ . (Proposition 2.5 of [1]).