Identifier
Mp00082:
Standard tableaux
—to Gelfand-Tsetlin pattern⟶
Gelfand-Tsetlin patterns
Mp00212: Gelfand-Tsetlin patterns —inverse cycle⟶ Gelfand-Tsetlin patterns
Mp00212: Gelfand-Tsetlin patterns —inverse cycle⟶ Gelfand-Tsetlin patterns
Images
[[1]] => [[1]] => [[1]]
[[1,2]] => [[2,0],[1]] => [[2,0],[1]]
[[1],[2]] => [[1,1],[1]] => [[1,1],[1]]
[[1,2,3]] => [[3,0,0],[2,0],[1]] => [[3,0,0],[2,0],[1]]
[[1,3],[2]] => [[2,1,0],[1,1],[1]] => [[2,1,0],[1,1],[1]]
[[1,2],[3]] => [[2,1,0],[2,0],[1]] => [[2,1,0],[2,0],[1]]
[[1],[2],[3]] => [[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]]
[[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => [[3,1,0,0],[2,1,0],[1,1],[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]]
[[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => [[3,1,0,0],[3,0,0],[2,0],[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]]
[[1,2],[3,4]] => [[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],[1,1,1],[1,1],[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]]
[[1,2],[3],[4]] => [[2,1,1,0],[2,1,0],[2,0],[1]] => [[2,1,1,0],[2,1,0],[2,0],[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]]
[[1,2,3,4,5]] => [[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]]
[[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],[3,1,0,0],[2,1,0],[1,1],[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],[2,1,0],[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],[3,0,0],[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],[4,0,0,0],[3,0,0],[2,0],[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],[2,2,0,0],[2,1,0],[1,1],[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],[2,2,0,0],[2,1,0],[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]]
[[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],[3,1,0,0],[2,1,0],[2,0],[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],[3,1,0,0],[3,0,0],[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],[2,1,1,0],[1,1,1],[1,1],[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],[2,1,1,0],[2,1,0],[1,1],[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]]
[[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]]
[[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],[3,1,0,0],[2,1,0],[2,0],[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],[3,1,0,0],[3,0,0],[2,0],[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],[2,1,1,0],[1,1,1],[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],[2,1,1,0],[2,1,0],[1,1],[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]]
[[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],[2,2,0,0],[2,1,0],[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],[2,2,0,0],[2,1,0],[2,0],[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],[1,1,1,1],[1,1,1],[1,1],[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],[1,1,1],[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],[2,1,0],[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],[2,1,1,0],[2,1,0],[2,0],[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]]
[[1,2,3,4,5,6]] => [[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]]
[[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],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[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],[3,1,0,0],[2,1,0],[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]]
[[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],[4,0,0,0],[3,0,0],[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],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[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],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[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],[3,2,0,0,0],[2,2,0,0],[2,1,0],[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],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[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]]
[[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]]
[[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]]
[[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],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[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],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[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],[4,1,0,0,0],[4,0,0,0],[3,0,0],[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],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[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],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[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],[2,1,1,0],[2,1,0],[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],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[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]]
[[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],[3,1,0,0],[3,0,0],[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]]
[[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],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[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],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[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],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[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]]
[[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],[2,2,0,0],[2,1,0],[2,0],[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],[3,1,0,0],[2,1,0],[1,1],[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]]
[[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]]
[[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],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[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],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[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],[2,2,1,0,0],[2,1,1,0],[2,1,0],[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],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[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],[2,2,1,0,0],[2,2,0,0],[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],[3,1,1,0,0],[2,1,1,0],[1,1,1],[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],[3,1,1,0,0],[2,1,1,0],[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],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[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],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[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],[3,1,1,0,0],[3,1,0,0],[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],[3,1,1,0,0],[3,1,0,0],[3,0,0],[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],[3,2,0,0,0],[2,2,0,0],[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],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[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],[3,2,0,0,0],[3,1,0,0],[2,1,0],[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],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[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],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[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],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[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],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[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],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[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]]
[[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],[2,1,1,0],[1,1,1],[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]]
[[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],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[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],[3,1,0,0],[2,1,0],[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],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[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],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[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]]
[[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]]
>>> 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
inverse cycle
Description
The inverse cycle action on a Gelfand-Tsetlin pattern.
Regard a Gelfand-Tsetlin pattern $p$ as an element of the $A_{m-1}$ crystal of shape $\lambda$, where $\lambda$ is the partition given by the first row of $p$ and $m$ is the width of $p$. Let $s_i(p)$ be the reflection of $p$ along its $i$-string, for $i\in\{1,\dots,m-1\}$. Then this map returns $c^{-1}(p)=s_{m-1}\dots s_2 s_1 (p)$.
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 $A_{m-1}$ crystal of shape $\lambda$, where $\lambda$ is the partition given by the first row of $p$ and $m$ is the width of $p$. Let $s_i(p)$ be the reflection of $p$ along its $i$-string, for $i\in\{1,\dots,m-1\}$. Then this map returns $c^{-1}(p)=s_{m-1}\dots s_2 s_1 (p)$.
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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