Identifier
-
Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000741: Graphs ⟶ ℤ
Values
[1,0] => [1,1,0,0] => [1,2] => ([],2) => 1
[1,0,1,0] => [1,1,0,1,0,0] => [3,1,2] => ([(0,2),(1,2)],3) => 2
[1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => ([],3) => 1
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [3,1,2,4] => ([(1,3),(2,3)],4) => 1
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => ([(1,3),(2,3)],4) => 1
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => ([],4) => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => 1
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => 1
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => 1
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => ([],5) => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => 1
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => 1
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => ([],6) => 1
[] => [1,0] => [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
The Colin de Verdière graph invariant.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!