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Identifier

Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux

Images

[] => []

[[1]] => [[1]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2,3,4,5]] => [[1,2,3,4,5]]

[[1,3,4,5],[2]] => [[1,2,3,4],[5]]

[[1,2,4,5],[3]] => [[1,2,3,5],[4]]

[[1,2,3,5],[4]] => [[1,2,4,5],[3]]

[[1,2,3,4],[5]] => [[1,3,4,5],[2]]

[[1,3,5],[2,4]] => [[1,2,4],[3,5]]

[[1,2,5],[3,4]] => [[1,2,3],[4,5]]

[[1,3,4],[2,5]] => [[1,3,4],[2,5]]

[[1,2,4],[3,5]] => [[1,3,5],[2,4]]

[[1,2,3],[4,5]] => [[1,2,5],[3,4]]

[[1,4,5],[2],[3]] => [[1,2,3],[4],[5]]

[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]]

[[1,2,5],[3],[4]] => [[1,2,5],[3],[4]]

[[1,3,4],[2],[5]] => [[1,3,4],[2],[5]]

[[1,2,4],[3],[5]] => [[1,3,5],[2],[4]]

[[1,2,3],[4],[5]] => [[1,4,5],[2],[3]]

[[1,4],[2,5],[3]] => [[1,3],[2,4],[5]]

[[1,3],[2,5],[4]] => [[1,2],[3,4],[5]]

[[1,2],[3,5],[4]] => [[1,2],[3,5],[4]]

[[1,3],[2,4],[5]] => [[1,4],[2,5],[3]]

[[1,2],[3,4],[5]] => [[1,3],[2,5],[4]]

[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]]

[[1,4],[2],[3],[5]] => [[1,3],[2],[4],[5]]

[[1,3],[2],[4],[5]] => [[1,4],[2],[3],[5]]

[[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]]

[[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]]

[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]]

[[1,3,4,5,6],[2]] => [[1,2,3,4,5],[6]]

[[1,2,4,5,6],[3]] => [[1,2,3,4,6],[5]]

[[1,2,3,5,6],[4]] => [[1,2,3,5,6],[4]]

[[1,2,3,4,6],[5]] => [[1,2,4,5,6],[3]]

[[1,2,3,4,5],[6]] => [[1,3,4,5,6],[2]]

[[1,3,5,6],[2,4]] => [[1,2,3,5],[4,6]]

[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]]

[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]]

[[1,2,4,6],[3,5]] => [[1,2,4,6],[3,5]]

[[1,2,3,6],[4,5]] => [[1,2,3,6],[4,5]]

[[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]]

[[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]]

[[1,2,3,5],[4,6]] => [[1,3,5,6],[2,4]]

[[1,2,3,4],[5,6]] => [[1,2,5,6],[3,4]]

[[1,4,5,6],[2],[3]] => [[1,2,3,4],[5],[6]]

[[1,3,5,6],[2],[4]] => [[1,2,3,5],[4],[6]]

[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]]

[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]]

[[1,2,4,6],[3],[5]] => [[1,2,4,6],[3],[5]]

[[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]]

[[1,3,4,5],[2],[6]] => [[1,3,4,5],[2],[6]]

[[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]]

[[1,2,3,5],[4],[6]] => [[1,3,5,6],[2],[4]]

[[1,2,3,4],[5],[6]] => [[1,4,5,6],[2],[3]]

[[1,3,5],[2,4,6]] => [[1,3,5],[2,4,6]]

[[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]]

[[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]]

[[1,2,4],[3,5,6]] => [[1,2,4],[3,5,6]]

[[1,2,3],[4,5,6]] => [[1,2,3],[4,5,6]]

[[1,4,6],[2,5],[3]] => [[1,2,4],[3,5],[6]]

[[1,3,6],[2,5],[4]] => [[1,2,3],[4,5],[6]]

[[1,2,6],[3,5],[4]] => [[1,2,3],[4,6],[5]]

[[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]]

[[1,2,6],[3,4],[5]] => [[1,2,4],[3,6],[5]]

[[1,4,5],[2,6],[3]] => [[1,3,4],[2,5],[6]]

[[1,3,5],[2,6],[4]] => [[1,3,5],[2,4],[6]]

[[1,2,5],[3,6],[4]] => [[1,3,6],[2,4],[5]]

[[1,3,4],[2,6],[5]] => [[1,2,5],[3,4],[6]]

[[1,2,4],[3,6],[5]] => [[1,2,6],[3,4],[5]]

[[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]]

[[1,3,5],[2,4],[6]] => [[1,3,5],[2,6],[4]]

[[1,2,5],[3,4],[6]] => [[1,3,4],[2,6],[5]]

[[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]]

[[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]]

[[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]]

[[1,5,6],[2],[3],[4]] => [[1,2,3],[4],[5],[6]]

[[1,4,6],[2],[3],[5]] => [[1,2,4],[3],[5],[6]]

[[1,3,6],[2],[4],[5]] => [[1,2,5],[3],[4],[6]]

[[1,2,6],[3],[4],[5]] => [[1,2,6],[3],[4],[5]]

[[1,4,5],[2],[3],[6]] => [[1,3,4],[2],[5],[6]]

[[1,3,5],[2],[4],[6]] => [[1,3,5],[2],[4],[6]]

[[1,2,5],[3],[4],[6]] => [[1,3,6],[2],[4],[5]]

[[1,3,4],[2],[5],[6]] => [[1,4,5],[2],[3],[6]]

[[1,2,4],[3],[5],[6]] => [[1,4,6],[2],[3],[5]]

[[1,2,3],[4],[5],[6]] => [[1,5,6],[2],[3],[4]]

[[1,4],[2,5],[3,6]] => [[1,4],[2,5],[3,6]]

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click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.

References

[1] wikipedia:Jeu_de_taquin

Properties

bijective, graded, involutive

Sage code

def mapping(elt):
    return elt.schuetzenberger_involution()

Weight

Created

Jan 26, 2020 at 12:31 by FindStatCrew

Updated

Jan 26, 2020 at 12:31 by Martin Rubey