Identifier
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Mp00036: Gelfand-Tsetlin patterns —to semistandard tableau⟶ Semistandard tableaux
Mp00107: Semistandard tableaux —catabolism⟶ Semistandard tableaux
Images
=>
Cc0007;cc-rep-0Cc0018;cc-rep-1Cc0019;cc-rep-2Cc0019;cc-rep-3
[[1]]=>[[1]]=>[[1]]=>[[1]] [[1,2]]=>[[2,0],[1]]=>[[1,2]]=>[[1,2]] [[1],[2]]=>[[1,1],[1]]=>[[1],[2]]=>[[1,2]] [[1,2,3]]=>[[3,0,0],[2,0],[1]]=>[[1,2,3]]=>[[1,2,3]] [[1,3],[2]]=>[[2,1,0],[1,1],[1]]=>[[1,3],[2]]=>[[1,2],[3]] [[1,2],[3]]=>[[2,1,0],[2,0],[1]]=>[[1,2],[3]]=>[[1,2,3]] [[1],[2],[3]]=>[[1,1,1],[1,1],[1]]=>[[1],[2],[3]]=>[[1,2],[3]] [[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4]]=>[[1,2,3,4]] [[1,3,4],[2]]=>[[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2]]=>[[1,2,4],[3]] [[1,2,4],[3]]=>[[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3]]=>[[1,2,3],[4]] [[1,2,3],[4]]=>[[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4]]=>[[1,2,3,4]] [[1,3],[2,4]]=>[[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4]]=>[[1,2,4],[3]] [[1,2],[3,4]]=>[[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4]]=>[[1,2,3,4]] [[1,4],[2],[3]]=>[[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]] [[1,3],[2],[4]]=>[[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4]]=>[[1,2,4],[3]] [[1,2],[3],[4]]=>[[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4]]=>[[1,2,3],[4]] [[1],[2],[3],[4]]=>[[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1],[2],[3],[4]]=>[[1,2],[3],[4]] [[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]] [[1,3,4,5],[2]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4,5],[2]]=>[[1,2,4,5],[3]] [[1,2,4,5],[3]]=>[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]] [[1,2,3,5],[4]]=>[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,5],[4]]=>[[1,2,3,4],[5]] [[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3,4],[5]]=>[[1,2,3,4,5]] [[1,3,5],[2,4]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]] [[1,2,5],[3,4]]=>[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3,4]]=>[[1,2,3,4],[5]] [[1,3,4],[2,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2,5]]=>[[1,2,4,5],[3]] [[1,2,4],[3,5]]=>[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3,5]]=>[[1,2,3,5],[4]] [[1,2,3],[4,5]]=>[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4,5]]=>[[1,2,3,4,5]] [[1,4,5],[2],[3]]=>[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4,5],[2],[3]]=>[[1,2,5],[3],[4]] [[1,3,5],[2],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]] [[1,2,5],[3],[4]]=>[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2,5],[3],[4]]=>[[1,2,3],[4],[5]] [[1,3,4],[2],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]=>[[1,3,4],[2],[5]]=>[[1,2,4,5],[3]] [[1,2,4],[3],[5]]=>[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]]=>[[1,2,4],[3],[5]]=>[[1,2,3,5],[4]] [[1,2,3],[4],[5]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]=>[[1,2,3],[4],[5]]=>[[1,2,3,4],[5]] [[1,4],[2,5],[3]]=>[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,5],[3]]=>[[1,2,5],[3],[4]] [[1,3],[2,5],[4]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,5],[4]]=>[[1,2,4,5],[3]] [[1,2],[3,5],[4]]=>[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4]]=>[[1,2,3,5],[4]] [[1,3],[2,4],[5]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5]]=>[[1,2,4],[3,5]] [[1,2],[3,4],[5]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5]]=>[[1,2,3,4],[5]] [[1,5],[2],[3],[4]]=>[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]] [[1,4],[2],[3],[5]]=>[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3],[5]]=>[[1,2,5],[3],[4]] [[1,3],[2],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4],[5]]=>[[1,2,4],[3],[5]] [[1,2],[3],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5]]=>[[1,2,3],[4],[5]] [[1],[2],[3],[4],[5]]=>[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5]] [[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]]=>[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]] [[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]]=>[[1,3,4,5,6],[2]]=>[[1,2,4,5,6],[3]] [[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]]=>[[1,2,4,5,6],[3]]=>[[1,2,3,5,6],[4]] [[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]]=>[[1,2,3,5,6],[4]]=>[[1,2,3,4,6],[5]] [[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]]=>[[1,2,3,4,6],[5]]=>[[1,2,3,4,5],[6]] [[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]]=>[[1,2,3,4,5],[6]]=>[[1,2,3,4,5,6]] [[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]]=>[[1,3,5,6],[2,4]]=>[[1,2,4,6],[3,5]] [[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]]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]] [[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]]=>[[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]] [[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]]=>[[1,2,4,6],[3,5]]=>[[1,2,3,5],[4,6]] [[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]]=>[[1,2,3,6],[4,5]]=>[[1,2,3,4,5],[6]] [[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]]=>[[1,3,4,5],[2,6]]=>[[1,2,4,5,6],[3]] [[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]]=>[[1,2,4,5],[3,6]]=>[[1,2,3,5,6],[4]] [[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]]=>[[1,2,3,5],[4,6]]=>[[1,2,3,4,6],[5]] [[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]]=>[[1,2,3,4],[5,6]]=>[[1,2,3,4,5,6]] [[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]]=>[[1,4,5,6],[2],[3]]=>[[1,2,5,6],[3],[4]] [[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]]=>[[1,3,5,6],[2],[4]]=>[[1,2,4,6],[3],[5]] [[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]]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]] [[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]]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]] [[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]]=>[[1,2,4,6],[3],[5]]=>[[1,2,3,5],[4],[6]] [[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]]=>[[1,2,3,6],[4],[5]]=>[[1,2,3,4],[5],[6]] [[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]]=>[[1,3,4,5],[2],[6]]=>[[1,2,4,5,6],[3]] [[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]]=>[[1,2,4,5],[3],[6]]=>[[1,2,3,5,6],[4]] [[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]]=>[[1,2,3,5],[4],[6]]=>[[1,2,3,4,6],[5]] [[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]]=>[[1,2,3,4],[5],[6]]=>[[1,2,3,4,5],[6]] [[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]]=>[[1,3,5],[2,4,6]]=>[[1,2,4,6],[3,5]] [[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]]=>[[1,2,5],[3,4,6]]=>[[1,2,3,4,6],[5]] [[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]]=>[[1,3,4],[2,5,6]]=>[[1,2,4,5,6],[3]] [[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]]=>[[1,2,4],[3,5,6]]=>[[1,2,3,5,6],[4]] [[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]]=>[[1,2,3],[4,5,6]]=>[[1,2,3,4,5,6]] [[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]]=>[[1,4,6],[2,5],[3]]=>[[1,2,5],[3,6],[4]] [[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]]=>[[1,3,6],[2,5],[4]]=>[[1,2,4,5],[3],[6]] [[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]]=>[[1,2,6],[3,5],[4]]=>[[1,2,3,5],[4],[6]] [[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]]=>[[1,3,6],[2,4],[5]]=>[[1,2,4],[3,5],[6]] [[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]]=>[[1,2,6],[3,4],[5]]=>[[1,2,3,4],[5],[6]] [[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]]=>[[1,4,5],[2,6],[3]]=>[[1,2,5,6],[3],[4]] [[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]]=>[[1,3,5],[2,6],[4]]=>[[1,2,4,6],[3],[5]] [[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]]=>[[1,2,5],[3,6],[4]]=>[[1,2,3,6],[4],[5]] [[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]]=>[[1,3,4],[2,6],[5]]=>[[1,2,4,5,6],[3]] [[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]]=>[[1,2,4],[3,6],[5]]=>[[1,2,3,5,6],[4]] [[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]]=>[[1,2,3],[4,6],[5]]=>[[1,2,3,4,6],[5]] [[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]]=>[[1,3,5],[2,4],[6]]=>[[1,2,4,6],[3,5]] [[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]]=>[[1,2,5],[3,4],[6]]=>[[1,2,3,4],[5,6]] [[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]]=>[[1,3,4],[2,5],[6]]=>[[1,2,4,5],[3,6]] [[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]]=>[[1,2,4],[3,5],[6]]=>[[1,2,3,5],[4,6]] [[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]]=>[[1,2,3],[4,5],[6]]=>[[1,2,3,4,5],[6]] [[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]]=>[[1,5,6],[2],[3],[4]]=>[[1,2,6],[3],[4],[5]] [[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]]=>[[1,4,6],[2],[3],[5]]=>[[1,2,5],[3],[4],[6]] [[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]]=>[[1,3,6],[2],[4],[5]]=>[[1,2,4],[3],[5],[6]] [[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]]=>[[1,2,6],[3],[4],[5]]=>[[1,2,3],[4],[5],[6]] [[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]]=>[[1,4,5],[2],[3],[6]]=>[[1,2,5,6],[3],[4]] [[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]]=>[[1,3,5],[2],[4],[6]]=>[[1,2,4,6],[3],[5]] [[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]]=>[[1,2,5],[3],[4],[6]]=>[[1,2,3,6],[4],[5]] [[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]]=>[[1,3,4],[2],[5],[6]]=>[[1,2,4,5],[3],[6]] [[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]]=>[[1,2,4],[3],[5],[6]]=>[[1,2,3,5],[4],[6]] [[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]]=>[[1,2,3],[4],[5],[6]]=>[[1,2,3,4],[5],[6]] [[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]]=>[[1,4],[2,5],[3,6]]=>[[1,2,5],[3,6],[4]] [[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]]=>[[1,3],[2,5],[4,6]]=>[[1,2,4,5],[3,6]] [[1,2],[3,5],[4,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4,6]]=>[[1,2,3,5],[4,6]] [[1,3],[2,4],[5,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5,6]]=>[[1,2,4,6],[3,5]] [[1,2],[3,4],[5,6]]=>[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5,6]]=>[[1,2,3,4],[5,6]] [[1,5],[2,6],[3],[4]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2,6],[3],[4]]=>[[1,2,6],[3],[4],[5]] [[1,4],[2,6],[3],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,6],[3],[5]]=>[[1,2,5,6],[3],[4]] [[1,3],[2,6],[4],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,6],[4],[5]]=>[[1,2,4,6],[3],[5]] [[1,2],[3,6],[4],[5]]=>[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,6],[4],[5]]=>[[1,2,3,6],[4],[5]] [[1,4],[2,5],[3],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4]] [[1,3],[2,5],[4],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,5],[4],[6]]=>[[1,2,4,5],[3],[6]] [[1,2],[3,5],[4],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,5],[4],[6]]=>[[1,2,3,5],[4],[6]] [[1,3],[2,4],[5],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]]=>[[1,3],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6]] [[1,2],[3,4],[5],[6]]=>[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]=>[[1,2],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6]] [[1,6],[2],[3],[4],[5]]=>[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]] [[1,5],[2],[3],[4],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]=>[[1,5],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5]] [[1,4],[2],[3],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]=>[[1,4],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6]] [[1,3],[2],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]]=>[[1,3],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6]] [[1,2],[3],[4],[5],[6]]=>[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]]=>[[1,2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6]] [[1],[2],[3],[4],[5],[6]]=>[[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]]=>[[1,2],[3],[4],[5],[6]]
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.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let $G$ be a Gelfand-Tsetlin pattern and let $\lambda^{(k)}$ be its $(n-k+1)$-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
$$ \lambda^{(0)} \subseteq \lambda^{(1)} \subseteq \cdots \subseteq \lambda^{(n)}, $$
where $\lambda^{(0)}$ is the empty partition.
Each skew shape $\lambda^{(k)} / \lambda^{(k-1)}$ is moreover a horizontal strip.
We now define a semistandard tableau $T(G)$ by inserting $k$ into the cells of the skew shape $\lambda^{(k)} / \lambda^{(k-1)}$, for $k=1,\dots,n$.
Map
catabolism
Description
Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).