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Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations

Images

[[1]] => [1]

[[2]] => [1]

[[3]] => [1]

[[4]] => [1]

[[5]] => [1]

[[6]] => [1]

[[1,1]] => [1,2]

[[1,2]] => [1,2]

[[2,2]] => [1,2]

[[1],[2]] => [2,1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,6]] => [1,2]

[[2,6]] => [1,2]

[[3,6]] => [1,2]

[[4,6]] => [1,2]

[[5,6]] => [1,2]

[[6,6]] => [1,2]

[[1],[6]] => [2,1]

[[2],[6]] => [2,1]

[[3],[6]] => [2,1]

[[4],[6]] => [2,1]

[[5],[6]] => [2,1]

[[1,7]] => [1,2]

[[2,7]] => [1,2]

[[3,7]] => [1,2]

[[4,7]] => [1,2]

[[5,7]] => [1,2]

[[6,7]] => [1,2]

[[7,7]] => [1,2]

[[1],[7]] => [2,1]

[[2],[7]] => [2,1]

[[3],[7]] => [2,1]

[[4],[7]] => [2,1]

[[5],[7]] => [2,1]

[[6],[7]] => [2,1]

[[1,8]] => [1,2]

[[2,8]] => [1,2]

[[3,8]] => [1,2]

[[4,8]] => [1,2]

[[5,8]] => [1,2]

[[6,8]] => [1,2]

[[7,8]] => [1,2]

[[8,8]] => [1,2]

[[1],[8]] => [2,1]

[[2],[8]] => [2,1]

[[3],[8]] => [2,1]

[[4],[8]] => [2,1]

[[5],[8]] => [2,1]

[[6],[8]] => [2,1]

[[7],[8]] => [2,1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).

Properties

graded

Sage code

def mapping(elt):
    return Permutation(elt.standardization().to_word())

Weight

Created

May 13, 2019 at 22:31 by Christian Stump

Updated

Jan 26, 2020 at 12:32 by Martin Rubey