Identifier
-
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤ
Values
[[1,2]] => [1,2] => [1,2] => 0
[[2,2]] => [1,2] => [1,2] => 0
[[1],[2]] => [2,1] => [2,1] => 0
[[1,3]] => [1,2] => [1,2] => 0
[[2,3]] => [1,2] => [1,2] => 0
[[3,3]] => [1,2] => [1,2] => 0
[[1],[3]] => [2,1] => [2,1] => 0
[[2],[3]] => [2,1] => [2,1] => 0
[[1,1,2]] => [1,2,3] => [1,2,3] => 0
[[1,2,2]] => [1,2,3] => [1,2,3] => 0
[[2,2,2]] => [1,2,3] => [1,2,3] => 0
[[1,1],[2]] => [3,1,2] => [3,1,2] => 0
[[1,2],[2]] => [2,1,3] => [2,1,3] => 0
[[1,4]] => [1,2] => [1,2] => 0
[[2,4]] => [1,2] => [1,2] => 0
[[3,4]] => [1,2] => [1,2] => 0
[[4,4]] => [1,2] => [1,2] => 0
[[1],[4]] => [2,1] => [2,1] => 0
[[2],[4]] => [2,1] => [2,1] => 0
[[3],[4]] => [2,1] => [2,1] => 0
[[1,1,3]] => [1,2,3] => [1,2,3] => 0
[[1,2,3]] => [1,2,3] => [1,2,3] => 0
[[1,3,3]] => [1,2,3] => [1,2,3] => 0
[[2,2,3]] => [1,2,3] => [1,2,3] => 0
[[2,3,3]] => [1,2,3] => [1,2,3] => 0
[[3,3,3]] => [1,2,3] => [1,2,3] => 0
[[1,1],[3]] => [3,1,2] => [3,1,2] => 0
[[1,2],[3]] => [3,1,2] => [3,1,2] => 0
[[1,3],[2]] => [2,1,3] => [2,1,3] => 0
[[1,3],[3]] => [2,1,3] => [2,1,3] => 0
[[2,2],[3]] => [3,1,2] => [3,1,2] => 0
[[2,3],[3]] => [2,1,3] => [2,1,3] => 0
[[1],[2],[3]] => [3,2,1] => [3,2,1] => 1
[[1,5]] => [1,2] => [1,2] => 0
[[2,5]] => [1,2] => [1,2] => 0
[[3,5]] => [1,2] => [1,2] => 0
[[4,5]] => [1,2] => [1,2] => 0
[[5,5]] => [1,2] => [1,2] => 0
[[1],[5]] => [2,1] => [2,1] => 0
[[2],[5]] => [2,1] => [2,1] => 0
[[3],[5]] => [2,1] => [2,1] => 0
[[4],[5]] => [2,1] => [2,1] => 0
[[1,1,4]] => [1,2,3] => [1,2,3] => 0
[[1,2,4]] => [1,2,3] => [1,2,3] => 0
[[1,3,4]] => [1,2,3] => [1,2,3] => 0
[[1,4,4]] => [1,2,3] => [1,2,3] => 0
[[2,2,4]] => [1,2,3] => [1,2,3] => 0
[[2,3,4]] => [1,2,3] => [1,2,3] => 0
[[2,4,4]] => [1,2,3] => [1,2,3] => 0
[[3,3,4]] => [1,2,3] => [1,2,3] => 0
[[3,4,4]] => [1,2,3] => [1,2,3] => 0
[[4,4,4]] => [1,2,3] => [1,2,3] => 0
[[1,1],[4]] => [3,1,2] => [3,1,2] => 0
[[1,2],[4]] => [3,1,2] => [3,1,2] => 0
[[1,4],[2]] => [2,1,3] => [2,1,3] => 0
[[1,3],[4]] => [3,1,2] => [3,1,2] => 0
[[1,4],[3]] => [2,1,3] => [2,1,3] => 0
[[1,4],[4]] => [2,1,3] => [2,1,3] => 0
[[2,2],[4]] => [3,1,2] => [3,1,2] => 0
[[2,3],[4]] => [3,1,2] => [3,1,2] => 0
[[2,4],[3]] => [2,1,3] => [2,1,3] => 0
[[2,4],[4]] => [2,1,3] => [2,1,3] => 0
[[3,3],[4]] => [3,1,2] => [3,1,2] => 0
[[3,4],[4]] => [2,1,3] => [2,1,3] => 0
[[1],[2],[4]] => [3,2,1] => [3,2,1] => 1
[[1],[3],[4]] => [3,2,1] => [3,2,1] => 1
[[2],[3],[4]] => [3,2,1] => [3,2,1] => 1
[[1,6]] => [1,2] => [1,2] => 0
[[2,6]] => [1,2] => [1,2] => 0
[[3,6]] => [1,2] => [1,2] => 0
[[4,6]] => [1,2] => [1,2] => 0
[[5,6]] => [1,2] => [1,2] => 0
[[6,6]] => [1,2] => [1,2] => 0
[[1],[6]] => [2,1] => [2,1] => 0
[[2],[6]] => [2,1] => [2,1] => 0
[[3],[6]] => [2,1] => [2,1] => 0
[[4],[6]] => [2,1] => [2,1] => 0
[[5],[6]] => [2,1] => [2,1] => 0
[[1,1,5]] => [1,2,3] => [1,2,3] => 0
[[1,2,5]] => [1,2,3] => [1,2,3] => 0
[[1,3,5]] => [1,2,3] => [1,2,3] => 0
[[1,4,5]] => [1,2,3] => [1,2,3] => 0
[[1,5,5]] => [1,2,3] => [1,2,3] => 0
[[2,2,5]] => [1,2,3] => [1,2,3] => 0
[[2,3,5]] => [1,2,3] => [1,2,3] => 0
[[2,4,5]] => [1,2,3] => [1,2,3] => 0
[[2,5,5]] => [1,2,3] => [1,2,3] => 0
[[3,3,5]] => [1,2,3] => [1,2,3] => 0
[[3,4,5]] => [1,2,3] => [1,2,3] => 0
[[3,5,5]] => [1,2,3] => [1,2,3] => 0
[[4,4,5]] => [1,2,3] => [1,2,3] => 0
[[4,5,5]] => [1,2,3] => [1,2,3] => 0
[[5,5,5]] => [1,2,3] => [1,2,3] => 0
[[1,1],[5]] => [3,1,2] => [3,1,2] => 0
[[1,2],[5]] => [3,1,2] => [3,1,2] => 0
[[1,5],[2]] => [2,1,3] => [2,1,3] => 0
[[1,3],[5]] => [3,1,2] => [3,1,2] => 0
[[1,5],[3]] => [2,1,3] => [2,1,3] => 0
[[1,4],[5]] => [3,1,2] => [3,1,2] => 0
[[1,5],[4]] => [2,1,3] => [2,1,3] => 0
[[1,5],[5]] => [2,1,3] => [2,1,3] => 0
>>> Load all 301 entries. <<<
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Description
The number of edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
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
to signed permutation
Description
The signed permutation with all signs positive.
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