Identifier
Values
[1,2,3] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
[1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 0
[1,2,4,3] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[1,3,2,4] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 0
[2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[2,3,1,4] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[2,4,1,3] => [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) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[3,1,4,2] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[3,2,4,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[3,4,2,1] => [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) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[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) => ([(2,5),(3,4)],6) => 0
[4,2,3,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
[4,3,1,2] => [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) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 1
search for individual values
searching the database for the individual values of this statistic
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Map
incomparability graph
Description
The incomparability graph of a poset.
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
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.