Identifier
Values
[[1]] => [1] => [1] => ([],1) => 1
[[1],[2]] => [2,1] => [2,1] => ([(0,1)],2) => 2
[[1],[2],[3]] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[1,3],[2],[4]] => [4,2,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 4
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 5
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 5
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 6
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [4,1,2,6,5,3] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 6
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [5,4,3,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [5,4,1,6,3,2] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [5,1,6,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [4,1,2,6,3,7,5] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => 7
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [5,4,1,6,2,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [5,1,6,4,2,7,3] => ([(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [5,4,1,2,7,6,3] => ([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 7
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [5,1,6,2,7,4,3] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [5,1,2,7,6,4,3] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 7
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [6,5,4,3,1,7,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [6,5,4,1,7,3,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [6,5,1,7,4,3,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [6,1,7,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 5
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 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 number of distinct eigenvalues of the distance Laplacian of a connected graph.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.