Identifier
Values
[1,0] => [2,1] => [1,2] => ([(0,1)],2) => 0
[1,0,1,0] => [3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[1,1,0,0] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 0
[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) => 0
[1,0,1,1,0,0] => [3,1,4,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 1
[1,1,0,0,1,0] => [2,4,1,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 1
[1,1,0,1,0,0] => [4,3,1,2] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 1
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 0
[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) => 0
[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) => 0
[] => [1] => [1] => ([],1) => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
Number of triples of incomparable elements in a finite poset.
For a finite poset this is the number of 3-element sets $S \in \binom{P}{3}$ that are pairwise incomparable.
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.