Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001534
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Mapping
St001534: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 1
([],2)
 => 0
([(0,1)],2)
 => 1
([],3)
 => 0
([(1,2)],3)
 => -1
([(0,1),(0,2)],3)
 => 0
([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => 0
([],4)
 => 0
([(2,3)],4)
 => 2
([(1,2),(1,3)],4)
 => 0
([(0,1),(0,2),(0,3)],4)
 => 0
([(0,2),(0,3),(3,1)],4)
 => -1
([(0,1),(0,2),(1,3),(2,3)],4)
 => 0
([(1,2),(2,3)],4)
 => -2
([(0,3),(3,1),(3,2)],4)
 => 0
([(1,3),(2,3)],4)
 => 0
([(0,3),(1,3),(3,2)],4)
 => 0
([(0,3),(1,3),(2,3)],4)
 => 0
([(0,3),(1,2)],4)
 => -2
([(0,3),(1,2),(1,3)],4)
 => -1
([(0,2),(0,3),(1,2),(1,3)],4)
 => 0
([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => -1
([],5)
 => 0
([(3,4)],5)
 => -6
([(2,3),(2,4)],5)
 => 0
([(1,2),(1,3),(1,4)],5)
 => 0
([(0,1),(0,2),(0,3),(0,4)],5)
 => 0
([(0,2),(0,3),(0,4),(4,1)],5)
 => 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 0
([(1,3),(1,4),(4,2)],5)
 => 3
([(0,3),(0,4),(4,1),(4,2)],5)
 => 0
([(1,2),(1,3),(2,4),(3,4)],5)
 => 0
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 0
([(0,3),(0,4),(3,2),(4,1)],5)
 => -2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => -1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 0
([(2,3),(3,4)],5)
 => 6
([(1,4),(4,2),(4,3)],5)
 => 0
([(0,4),(4,1),(4,2),(4,3)],5)
 => 0
([(2,4),(3,4)],5)
 => 0
([(1,4),(2,4),(4,3)],5)
 => 0
([(0,4),(1,4),(4,2),(4,3)],5)
 => 0
([(1,4),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,4),(4,3)],5)
 => 0
([(0,4),(1,4),(2,4),(3,4)],5)
 => 0
([(0,4),(1,4),(2,3)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => 0
Description
The alternating sum of the coefficients of the Poincare polynomial of the poset cone. For a poset $P$ on $\{1,\dots,n\}$, let $\mathcal K_P = \{\vec x\in\mathbb R^n| x_i < x_j \text{ for } i < _P j\}$. Furthermore let $\mathcal L(\mathcal A)$ be the intersection lattice of the braid arrangement $A_{n-1}$ and let $\mathcal L^{int} = \{ X \in \mathcal L(\mathcal A) | X \cap \mathcal K_P \neq \emptyset \}$. Then the Poincare polynomial of the poset cone is $Poin(t) = \sum_{X\in\mathcal L^{int}} |\mu(0, X)| t^{codim X}$. This statistic records its $Poin(-1)$.