- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs

Images

[[1,2]] => [1,2] => ([],2)

[[2,2]] => [1,2] => ([],2)

[[1],[2]] => [2,1] => ([(0,1)],2)

[[1,3]] => [1,2] => ([],2)

[[2,3]] => [1,2] => ([],2)

[[3,3]] => [1,2] => ([],2)

[[1],[3]] => [2,1] => ([(0,1)],2)

[[2],[3]] => [2,1] => ([(0,1)],2)

[[1,1,2]] => [1,2,3] => ([],3)

[[1,2,2]] => [1,2,3] => ([],3)

[[2,2,2]] => [1,2,3] => ([],3)

[[1,1],[2]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,2],[2]] => [2,1,3] => ([(1,2)],3)

[[1,4]] => [1,2] => ([],2)

[[2,4]] => [1,2] => ([],2)

[[3,4]] => [1,2] => ([],2)

[[4,4]] => [1,2] => ([],2)

[[1],[4]] => [2,1] => ([(0,1)],2)

[[2],[4]] => [2,1] => ([(0,1)],2)

[[3],[4]] => [2,1] => ([(0,1)],2)

[[1,1,3]] => [1,2,3] => ([],3)

[[1,2,3]] => [1,2,3] => ([],3)

[[1,3,3]] => [1,2,3] => ([],3)

[[2,2,3]] => [1,2,3] => ([],3)

[[2,3,3]] => [1,2,3] => ([],3)

[[3,3,3]] => [1,2,3] => ([],3)

[[1,1],[3]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,2],[3]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,3],[2]] => [2,1,3] => ([(1,2)],3)

[[1,3],[3]] => [2,1,3] => ([(1,2)],3)

[[2,2],[3]] => [3,1,2] => ([(0,2),(1,2)],3)

[[2,3],[3]] => [2,1,3] => ([(1,2)],3)

[[1],[2],[3]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)

[[1,1,1,2]] => [1,2,3,4] => ([],4)

[[1,1,2,2]] => [1,2,3,4] => ([],4)

[[1,2,2,2]] => [1,2,3,4] => ([],4)

[[2,2,2,2]] => [1,2,3,4] => ([],4)

[[1,1,1],[2]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)

[[1,1,2],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4)

[[1,2,2],[2]] => [2,1,3,4] => ([(2,3)],4)

[[1,1],[2,2]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)

[[1,5]] => [1,2] => ([],2)

[[2,5]] => [1,2] => ([],2)

[[3,5]] => [1,2] => ([],2)

[[4,5]] => [1,2] => ([],2)

[[5,5]] => [1,2] => ([],2)

[[1],[5]] => [2,1] => ([(0,1)],2)

[[2],[5]] => [2,1] => ([(0,1)],2)

[[3],[5]] => [2,1] => ([(0,1)],2)

[[4],[5]] => [2,1] => ([(0,1)],2)

[[1,1,4]] => [1,2,3] => ([],3)

[[1,2,4]] => [1,2,3] => ([],3)

[[1,3,4]] => [1,2,3] => ([],3)

[[1,4,4]] => [1,2,3] => ([],3)

[[2,2,4]] => [1,2,3] => ([],3)

[[2,3,4]] => [1,2,3] => ([],3)

[[2,4,4]] => [1,2,3] => ([],3)

[[3,3,4]] => [1,2,3] => ([],3)

[[3,4,4]] => [1,2,3] => ([],3)

[[4,4,4]] => [1,2,3] => ([],3)

[[1,1],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,2],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,4],[2]] => [2,1,3] => ([(1,2)],3)

[[1,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[1,4],[3]] => [2,1,3] => ([(1,2)],3)

[[1,4],[4]] => [2,1,3] => ([(1,2)],3)

[[2,2],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[2,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[2,4],[3]] => [2,1,3] => ([(1,2)],3)

[[2,4],[4]] => [2,1,3] => ([(1,2)],3)

[[3,3],[4]] => [3,1,2] => ([(0,2),(1,2)],3)

[[3,4],[4]] => [2,1,3] => ([(1,2)],3)

[[1],[2],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)

[[1],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)

[[2],[3],[4]] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)

[[1,1,1,3]] => [1,2,3,4] => ([],4)

[[1,1,2,3]] => [1,2,3,4] => ([],4)

[[1,1,3,3]] => [1,2,3,4] => ([],4)

[[1,2,2,3]] => [1,2,3,4] => ([],4)

[[1,2,3,3]] => [1,2,3,4] => ([],4)

[[1,3,3,3]] => [1,2,3,4] => ([],4)

[[2,2,2,3]] => [1,2,3,4] => ([],4)

[[2,2,3,3]] => [1,2,3,4] => ([],4)

[[2,3,3,3]] => [1,2,3,4] => ([],4)

[[3,3,3,3]] => [1,2,3,4] => ([],4)

[[1,1,1],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)

[[1,1,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)

[[1,1,3],[2]] => [3,1,2,4] => ([(1,3),(2,3)],4)

[[1,1,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4)

[[1,2,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)

[[1,2,3],[2]] => [2,1,3,4] => ([(2,3)],4)

[[1,2,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4)

[[1,3,3],[2]] => [2,1,3,4] => ([(2,3)],4)

[[1,3,3],[3]] => [2,1,3,4] => ([(2,3)],4)

[[2,2,2],[3]] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)

[[2,2,3],[3]] => [3,1,2,4] => ([(1,3),(2,3)],4)

[[2,3,3],[3]] => [2,1,3,4] => ([(2,3)],4)

[[1,1],[2,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)

[[1,1],[3,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)

[[1,2],[2,3]] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)

[[1,2],[3,3]] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)

>>> Load all 2507 entries. <<<

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost 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.