Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000525
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Mapping
St000525: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],2)
 => 1
([(0,1)],2)
 => 1
([],3)
 => 1
([(1,2)],3)
 => 1
([(0,1),(0,2)],3)
 => 2
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 2
([],4)
 => 1
([(2,3)],4)
 => 1
([(1,2),(1,3)],4)
 => 3
([(0,1),(0,2),(0,3)],4)
 => 3
([(0,2),(0,3),(3,1)],4)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
([(1,2),(2,3)],4)
 => 1
([(0,3),(3,1),(3,2)],4)
 => 3
([(1,3),(2,3)],4)
 => 3
([(0,3),(1,3),(3,2)],4)
 => 3
([(0,3),(1,3),(2,3)],4)
 => 3
([(0,3),(1,2)],4)
 => 3
([(0,3),(1,2),(1,3)],4)
 => 3
([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => 2
([],5)
 => 1
([(3,4)],5)
 => 1
([(2,3),(2,4)],5)
 => 3
([(1,2),(1,3),(1,4)],5)
 => 5
([(0,1),(0,2),(0,3),(0,4)],5)
 => 7
([(0,2),(0,3),(0,4),(4,1)],5)
 => 5
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 8
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 5
([(1,3),(1,4),(4,2)],5)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => 8
([(1,2),(1,3),(2,4),(3,4)],5)
 => 3
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 4
([(0,3),(0,4),(3,2),(4,1)],5)
 => 8
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 5
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 3
([(2,3),(3,4)],5)
 => 1
([(1,4),(4,2),(4,3)],5)
 => 3
([(0,4),(4,1),(4,2),(4,3)],5)
 => 5
([(2,4),(3,4)],5)
 => 3
([(1,4),(2,4),(4,3)],5)
 => 3
([(0,4),(1,4),(4,2),(4,3)],5)
 => 3
([(1,4),(2,4),(3,4)],5)
 => 5
([(0,4),(1,4),(2,4),(4,3)],5)
 => 5
([(0,4),(1,4),(2,4),(3,4)],5)
 => 7
([(0,4),(1,4),(2,3)],5)
 => 5
([(0,4),(1,3),(2,3),(2,4)],5)
 => 7
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
Description
The number of posets with the same zeta polynomial. The zeta polynomial $Z$ is the polynomial such that $Z(m)$ is the number of weakly increasing sequences $x_1\leq x_2\leq\dots\leq x_{m−1}$ of elements of the poset. See section 3.12 of [1]. Since $$ Z(q) = \sum_{k\geq 1} \binom{q-2}{k-1} c_k, $$ where $c_k$ is the number of chains of length $k$, this statistic is the same as the number of posets with the same chain polynomial.