Identifier
Mp00082:
Standard tableaux
—to Gelfand-Tsetlin pattern⟶
Gelfand-Tsetlin patterns
Mp00078: Gelfand-Tsetlin patterns —Schuetzenberger involution⟶ Gelfand-Tsetlin patterns
Mp00212: Gelfand-Tsetlin patterns —inverse cycle⟶ Gelfand-Tsetlin patterns
Mp00078: Gelfand-Tsetlin patterns —Schuetzenberger involution⟶ Gelfand-Tsetlin patterns
Mp00212: Gelfand-Tsetlin patterns —inverse cycle⟶ Gelfand-Tsetlin patterns
Images
[[1]] => [[1]] => [[1]] => [[1]]
[[1,2]] => [[2,0],[1]] => [[2,0],[1]] => [[2,0],[1]]
[[1],[2]] => [[1,1],[1]] => [[1,1],[1]] => [[1,1],[1]]
[[1,2,3]] => [[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]]
[[1,3],[2]] => [[2,1,0],[1,1],[1]] => [[2,1,0],[2,0],[1]] => [[2,1,0],[2,0],[1]]
[[1,2],[3]] => [[2,1,0],[2,0],[1]] => [[2,1,0],[1,1],[1]] => [[2,1,0],[1,1],[1]]
[[1],[2],[3]] => [[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]]
[[1,2,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4],[2],[3]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2],[4]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,0],[1,1,1],[1,1],[1]]
[[1],[2],[3],[4]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,4,5],[3]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5],[4]] => [[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,4],[5]] => [[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,5],[2,4]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,5],[3,4]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4],[2,5]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3,5]] => [[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,3],[4,5]] => [[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2],[3]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,5],[2],[4]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,5],[3],[4]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4],[2],[5]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4],[3],[5]] => [[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,3],[4],[5]] => [[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,4],[2,5],[3]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3],[2,5],[4]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2],[3,5],[4]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3],[2,4],[5]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2],[3,4],[5]] => [[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,5],[2],[3],[4]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4],[2],[3],[5]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,3],[2],[4],[5]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2],[3],[4],[5]] => [[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1],[2],[3],[4],[5]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,2,3,4,5,6]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5,6],[2]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,4,5,6],[3]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,5,6],[4]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,3,4,6],[5]] => [[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,4,5],[6]] => [[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,5,6],[2,4]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,5,6],[3,4]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,6],[2,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,6],[3,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4,5]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,5],[2,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,3,5],[4,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,3,4],[5,6]] => [[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,4,5,6],[2],[3]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
[[1,3,5,6],[2],[4]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,5,6],[3],[4]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,4,6],[2],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,4,6],[3],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3,6],[4],[5]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,4,5],[2],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,4,5],[3],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,2,3,5],[4],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,3,4],[5],[6]] => [[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3,5],[2,4,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4],[2,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,4],[3,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,5,6]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2,5],[3]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2,5],[4]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,2,6],[3,5],[4]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,3,6],[2,4],[5]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,2,6],[3,4],[5]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2,6],[3]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,5],[2,6],[4]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,6],[4]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]
[[1,3,4],[2,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,4],[3,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
[[1,2,3],[4,6],[5]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,3,5],[2,4],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3,4],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,4],[2,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2,4],[3,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2,3],[4,5],[6]] => [[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,5,6],[2],[3],[4]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
[[1,4,6],[2],[3],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]
[[1,3,6],[2],[4],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,2,6],[3],[4],[5]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]
[[1,4,5],[2],[3],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
[[1,3,5],[2],[4],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,2,5],[3],[4],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]
[[1,3,4],[2],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2,4],[3],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,2,3],[4],[5],[6]] => [[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
[[1,4],[2,5],[3,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
[[1,3],[2,5],[4,6]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
>>> Load all 119 entries. <<<Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
Map
Schuetzenberger involution
Description
Applies the Schuetzenberger involution to a Gelfand-Tsetlin pattern.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type A it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than n. Use Schuetzenberger's jeu de taquin to slide all entries equal to 1 to the outer border of the tableau. Do the same for all entries equal to 2, restricting the tableau to the entries larger than 2, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to n, that is, replace e with n+1−e.
The Schuetzenberger involution is usually regarded as an involution on semistandard Young tableaux with a fixed bound on the size of the entries. It is also known as evacuation, and in the context of crystal graphs of type A it realizes Lusztig's involution.
In the language of tableaux it is defined as follows. Consider a semistandard tableau with no entry larger than n. Use Schuetzenberger's jeu de taquin to slide all entries equal to 1 to the outer border of the tableau. Do the same for all entries equal to 2, restricting the tableau to the entries larger than 2, and so on, until the tableau is a reverse semistandard tableau. Finally, replace each entry with its complement with respect to n, that is, replace e with n+1−e.
Map
inverse cycle
Description
The inverse cycle action on a Gelfand-Tsetlin pattern.
Regard a Gelfand-Tsetlin pattern p as an element of the Am−1 crystal of shape λ, where λ is the partition given by the first row of p and m is the width of p. Let si(p) be the reflection of p along its i-string, for i∈{1,…,m−1}. Then this map returns c−1(p)=sm−1…s2s1(p).
The order of this action is the width of the pattern. As a map on semistandard tableaux, it preserves the shape. Moreover, the weight of c−1(p) is the same as the weight of the inverse promotion of p.
Regard a Gelfand-Tsetlin pattern p as an element of the Am−1 crystal of shape λ, where λ is the partition given by the first row of p and m is the width of p. Let si(p) be the reflection of p along its i-string, for i∈{1,…,m−1}. Then this map returns c−1(p)=sm−1…s2s1(p).
The order of this action is the width of the pattern. As a map on semistandard tableaux, it preserves the shape. Moreover, the weight of c−1(p) is the same as the weight of the inverse promotion of p.
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