Identifier
Values
[1,0] => [2,1] => [1,2] => ([(0,1)],2) => 3
[1,0,1,0] => [3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 6
[1,1,0,0] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 4
[1,0,1,0,1,0] => [4,1,2,3] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 10
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 5
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 6
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 7
[] => [1] => [1] => ([],1) => 2
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Description
The number of facets in the chain polytope of the poset.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.