Processing math: 100%

Identifier
Values
[1] => [1,0,1,0] => [2,1] => ([(0,1)],2) => 1
[2,1] => [1,0,1,0,1,0] => [2,3,1] => ([(0,2),(1,2)],3) => 2
[3,1] => [1,1,0,1,0,0,1,0] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 1
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => 1
[3,2] => [1,1,0,0,1,0,1,0] => [1,3,4,2] => ([(1,3),(2,3)],4) => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => ([(1,3),(2,3)],4) => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => 1
[3,2,1] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => 1
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => 1
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => 1
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => 1
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 1
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => 1
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => 1
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => 1
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => 1
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => 1
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => 1
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => 1
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => 1
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 1
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => 1
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => 1
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => 1
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6) => 1
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6) => 1
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => 1
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => 1
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => 1
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => 1
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6) => 1
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
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
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of {1,…,n}, this is the graph with vertices {1,…,n}, where (i,j) is an edge if and only if it is an inversion of the permutation.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.