- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$