Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0018;cc-rep-2
[1]=>[[1]]=>[[1]] [2]=>[[1,2]]=>[[2,0],[1]] [1,1]=>[[1],[2]]=>[[1,1],[1]] [3]=>[[1,2,3]]=>[[3,0,0],[2,0],[1]] [2,1]=>[[1,2],[3]]=>[[2,1,0],[2,0],[1]] [1,1,1]=>[[1],[2],[3]]=>[[1,1,1],[1,1],[1]] [4]=>[[1,2,3,4]]=>[[4,0,0,0],[3,0,0],[2,0],[1]] [3,1]=>[[1,2,3],[4]]=>[[3,1,0,0],[3,0,0],[2,0],[1]] [2,2]=>[[1,2],[3,4]]=>[[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1]=>[[1,2],[3],[4]]=>[[2,1,1,0],[2,1,0],[2,0],[1]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[[1,1,1,1],[1,1,1],[1,1],[1]] [5]=>[[1,2,3,4,5]]=>[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,1]=>[[1,2,3,4],[5]]=>[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,2]=>[[1,2,3],[4,5]]=>[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,1,1]=>[[1,2,3],[4],[5]]=>[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,1]=>[[1,2],[3,4],[5]]=>[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[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]] [6]=>[[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]] [5,1]=>[[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]] [4,2]=>[[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]] [4,1,1]=>[[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]] [3,3]=>[[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]] [3,2,1]=>[[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]] [3,1,1,1]=>[[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]] [2,2,2]=>[[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]] [2,2,1,1]=>[[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]] [2,1,1,1,1]=>[[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]] [1,1,1,1,1,1]=>[[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]] [7]=>[[1,2,3,4,5,6,7]]=>[[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,1]=>[[1,2,3,4,5,6],[7]]=>[[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2]=>[[1,2,3,4,5],[6,7]]=>[[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3]=>[[1,2,3,4],[5,6,7]]=>[[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[[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]] [8]=>[[1,2,3,4,5,6,7,8]]=>[[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,1]=>[[1,2,3,4,5,6,7],[8]]=>[[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[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]] [9]=>[[1,2,3,4,5,6,7,8,9]]=>[[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[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]] [10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[8,1,1,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[7,2,1,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[7,1,1,1,0,0,0,0,0,0],[7,1,1,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[6,3,1,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[6,2,2,0,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[6,2,1,1,0,0,0,0,0,0],[6,2,1,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[6,1,1,1,1,0,0,0,0,0],[6,1,1,1,0,0,0,0,0],[6,1,1,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[5,5,0,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[5,2,1,1,1,0,0,0,0,0],[5,2,1,1,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[5,1,1,1,1,1,0,0,0,0],[5,1,1,1,1,0,0,0,0],[5,1,1,1,0,0,0,0],[5,1,1,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[[4,4,1,1,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[4,2,1,1,1,1,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[4,1,1,1,1,1,1,0,0,0],[4,1,1,1,1,1,0,0,0],[4,1,1,1,1,0,0,0],[4,1,1,1,0,0,0],[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[[3,3,2,2,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[[3,3,1,1,1,1,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[[3,2,2,2,1,0,0,0,0,0],[3,2,2,2,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[[3,2,2,1,1,1,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[[3,2,1,1,1,1,1,0,0,0],[3,2,1,1,1,1,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[3,1,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,1,0,0],[3,1,1,1,1,1,0,0],[3,1,1,1,1,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[[2,2,2,2,1,1,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[[2,2,2,1,1,1,1,0,0,0],[2,2,2,1,1,1,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[[2,2,1,1,1,1,1,1,0,0],[2,2,1,1,1,1,1,0,0],[2,2,1,1,1,1,0,0],[2,2,1,1,1,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[2,1,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,1,0],[2,1,1,1,1,1,1,0],[2,1,1,1,1,1,0],[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[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],[1,1,1,1],[1,1,1],[1,1],[1]] [5,4,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11]]=>[[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11]]=>[[5,4,1,1,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,3]=>[[1,2,3,4,5],[6,7,8],[9,10,11]]=>[[5,3,3,0,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11]]=>[[5,3,2,1,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,1,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10],[11]]=>[[5,3,1,1,1,0,0,0,0,0,0],[5,3,1,1,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,2,2]=>[[1,2,3,4,5],[6,7],[8,9],[10,11]]=>[[5,2,2,2,0,0,0,0,0,0,0],[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,2,1,1]=>[[1,2,3,4,5],[6,7],[8,9],[10],[11]]=>[[5,2,2,1,1,0,0,0,0,0,0],[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,3]=>[[1,2,3,4],[5,6,7,8],[9,10,11]]=>[[4,4,3,0,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11]]=>[[4,4,2,1,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,1,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10],[11]]=>[[4,4,1,1,1,0,0,0,0,0,0],[4,4,1,1,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,3,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11]]=>[[4,3,3,1,0,0,0,0,0,0,0],[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,2,2]=>[[1,2,3,4],[5,6,7],[8,9],[10,11]]=>[[4,3,2,2,0,0,0,0,0,0,0],[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,2,1,1]=>[[1,2,3,4],[5,6,7],[8,9],[10],[11]]=>[[4,3,2,1,1,0,0,0,0,0,0],[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11]]=>[[4,2,2,2,1,0,0,0,0,0,0],[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,3,2]=>[[1,2,3],[4,5,6],[7,8,9],[10,11]]=>[[3,3,3,2,0,0,0,0,0,0,0],[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,3,1,1]=>[[1,2,3],[4,5,6],[7,8,9],[10],[11]]=>[[3,3,3,1,1,0,0,0,0,0,0],[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,2,2,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11]]=>[[3,3,2,2,1,0,0,0,0,0,0],[3,3,2,2,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[[12,0,0,0,0,0,0,0,0,0,0,0],[11,0,0,0,0,0,0,0,0,0,0],[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[6,6,0,0,0,0,0,0,0,0,0,0],[6,5,0,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [6,4,2]=>[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[[6,4,2,0,0,0,0,0,0,0,0,0],[6,4,1,0,0,0,0,0,0,0,0],[6,4,0,0,0,0,0,0,0,0],[6,3,0,0,0,0,0,0,0],[6,2,0,0,0,0,0,0],[6,1,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,3]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12]]=>[[5,4,3,0,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12]]=>[[5,4,2,1,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,1,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10],[11],[12]]=>[[5,4,1,1,1,0,0,0,0,0,0,0],[5,4,1,1,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,3,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12]]=>[[5,3,3,1,0,0,0,0,0,0,0,0],[5,3,3,0,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,2,2]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12]]=>[[5,3,2,2,0,0,0,0,0,0,0,0],[5,3,2,1,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,2,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11],[12]]=>[[5,3,2,1,1,0,0,0,0,0,0,0],[5,3,2,1,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,2,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10,11],[12]]=>[[5,2,2,2,1,0,0,0,0,0,0,0],[5,2,2,2,0,0,0,0,0,0,0],[5,2,2,1,0,0,0,0,0,0],[5,2,2,0,0,0,0,0,0],[5,2,1,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,3,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12]]=>[[4,4,3,1,0,0,0,0,0,0,0,0],[4,4,3,0,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,2,2]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[[4,4,2,2,0,0,0,0,0,0,0,0],[4,4,2,1,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,2,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11],[12]]=>[[4,4,2,1,1,0,0,0,0,0,0,0],[4,4,2,1,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,3,2]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12]]=>[[4,3,3,2,0,0,0,0,0,0,0,0],[4,3,3,1,0,0,0,0,0,0,0],[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,3,1,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11],[12]]=>[[4,3,3,1,1,0,0,0,0,0,0,0],[4,3,3,1,0,0,0,0,0,0,0],[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,2,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10,11],[12]]=>[[4,3,2,2,1,0,0,0,0,0,0,0],[4,3,2,2,0,0,0,0,0,0,0],[4,3,2,1,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[[4,2,2,2,2,0,0,0,0,0,0,0],[4,2,2,2,1,0,0,0,0,0,0],[4,2,2,2,0,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[4,2,2,0,0,0,0,0],[4,2,1,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [3,3,3,2,1]=>[[1,2,3],[4,5,6],[7,8,9],[10,11],[12]]=>[[3,3,3,2,1,0,0,0,0,0,0,0],[3,3,3,2,0,0,0,0,0,0,0],[3,3,3,1,0,0,0,0,0,0],[3,3,3,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [3,3,2,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]]=>[[3,3,2,2,1,1,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,3,2,2,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,3,1,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] [2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[2,2,2,2,2,2,0,0,0,0,0,0],[2,2,2,2,2,1,0,0,0,0,0],[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[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],[1,1,1,1,1,1,1,1],[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]] [5,4,3,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13]]=>[[5,4,3,1,0,0,0,0,0,0,0,0,0],[5,4,3,0,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,2,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13]]=>[[5,4,2,2,0,0,0,0,0,0,0,0,0],[5,4,2,1,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,2,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12],[13]]=>[[5,4,2,1,1,0,0,0,0,0,0,0,0],[5,4,2,1,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13]]=>[[5,3,3,2,0,0,0,0,0,0,0,0,0],[5,3,3,1,0,0,0,0,0,0,0,0],[5,3,3,0,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12],[13]]=>[[5,3,3,1,1,0,0,0,0,0,0,0,0],[5,3,3,1,0,0,0,0,0,0,0,0],[5,3,3,0,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,2,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]=>[[5,3,2,2,1,0,0,0,0,0,0,0,0],[5,3,2,2,0,0,0,0,0,0,0,0],[5,3,2,1,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,3,2]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13]]=>[[4,4,3,2,0,0,0,0,0,0,0,0,0],[4,4,3,1,0,0,0,0,0,0,0,0],[4,4,3,0,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,3,1,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12],[13]]=>[[4,4,3,1,1,0,0,0,0,0,0,0,0],[4,4,3,1,0,0,0,0,0,0,0,0],[4,4,3,0,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,2,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10],[11,12],[13]]=>[[4,4,2,2,1,0,0,0,0,0,0,0,0],[4,4,2,2,0,0,0,0,0,0,0,0],[4,4,2,1,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,3,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9,10],[11,12],[13]]=>[[4,3,3,2,1,0,0,0,0,0,0,0,0],[4,3,3,2,0,0,0,0,0,0,0,0],[4,3,3,1,0,0,0,0,0,0,0],[4,3,3,0,0,0,0,0,0,0],[4,3,2,0,0,0,0,0,0],[4,3,1,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [7,7]=>[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]]=>[[7,7,0,0,0,0,0,0,0,0,0,0,0,0],[7,6,0,0,0,0,0,0,0,0,0,0,0],[7,5,0,0,0,0,0,0,0,0,0,0],[7,4,0,0,0,0,0,0,0,0,0],[7,3,0,0,0,0,0,0,0,0],[7,2,0,0,0,0,0,0,0],[7,1,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,3,2]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14]]=>[[5,4,3,2,0,0,0,0,0,0,0,0,0,0],[5,4,3,1,0,0,0,0,0,0,0,0,0],[5,4,3,0,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,3,1,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13],[14]]=>[[5,4,3,1,1,0,0,0,0,0,0,0,0,0],[5,4,3,1,0,0,0,0,0,0,0,0,0],[5,4,3,0,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,4,2,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11],[12,13],[14]]=>[[5,4,2,2,1,0,0,0,0,0,0,0,0,0],[5,4,2,2,0,0,0,0,0,0,0,0,0],[5,4,2,1,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [5,3,3,2,1]=>[[1,2,3,4,5],[6,7,8],[9,10,11],[12,13],[14]]=>[[5,3,3,2,1,0,0,0,0,0,0,0,0,0],[5,3,3,2,0,0,0,0,0,0,0,0,0],[5,3,3,1,0,0,0,0,0,0,0,0],[5,3,3,0,0,0,0,0,0,0,0],[5,3,2,0,0,0,0,0,0,0],[5,3,1,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [4,4,3,2,1]=>[[1,2,3,4],[5,6,7,8],[9,10,11],[12,13],[14]]=>[[4,4,3,2,1,0,0,0,0,0,0,0,0,0],[4,4,3,2,0,0,0,0,0,0,0,0,0],[4,4,3,1,0,0,0,0,0,0,0,0],[4,4,3,0,0,0,0,0,0,0,0],[4,4,2,0,0,0,0,0,0,0],[4,4,1,0,0,0,0,0,0],[4,4,0,0,0,0,0,0],[4,3,0,0,0,0,0],[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14]]=>[[2,2,2,2,2,2,2,0,0,0,0,0,0,0],[2,2,2,2,2,2,1,0,0,0,0,0,0],[2,2,2,2,2,2,0,0,0,0,0,0],[2,2,2,2,2,1,0,0,0,0,0],[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [5,4,3,2,1]=>[[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]=>[[5,4,3,2,1,0,0,0,0,0,0,0,0,0,0],[5,4,3,2,0,0,0,0,0,0,0,0,0,0],[5,4,3,1,0,0,0,0,0,0,0,0,0],[5,4,3,0,0,0,0,0,0,0,0,0],[5,4,2,0,0,0,0,0,0,0,0],[5,4,1,0,0,0,0,0,0,0],[5,4,0,0,0,0,0,0,0],[5,3,0,0,0,0,0,0],[5,2,0,0,0,0,0],[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [8,8]=>[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]=>[[8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,7,0,0,0,0,0,0,0,0,0,0,0,0,0],[8,6,0,0,0,0,0,0,0,0,0,0,0,0],[8,5,0,0,0,0,0,0,0,0,0,0,0],[8,4,0,0,0,0,0,0,0,0,0,0],[8,3,0,0,0,0,0,0,0,0,0],[8,2,0,0,0,0,0,0,0,0],[8,1,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16]]=>[[2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,1,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,0,0,0,0,0,0,0],[2,2,2,2,2,2,1,0,0,0,0,0,0],[2,2,2,2,2,2,0,0,0,0,0,0],[2,2,2,2,2,1,0,0,0,0,0],[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18]]=>[[2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,1,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,1,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,0,0,0,0,0,0,0],[2,2,2,2,2,2,1,0,0,0,0,0,0],[2,2,2,2,2,2,0,0,0,0,0,0],[2,2,2,2,2,1,0,0,0,0,0],[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [2,2,2,2,2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12],[13,14],[15,16],[17,18],[19,20]]=>[[2,2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,1,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,1,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,2,0,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,1,0,0,0,0,0,0,0],[2,2,2,2,2,2,2,0,0,0,0,0,0,0],[2,2,2,2,2,2,1,0,0,0,0,0,0],[2,2,2,2,2,2,0,0,0,0,0,0],[2,2,2,2,2,1,0,0,0,0,0],[2,2,2,2,2,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,2,0,0,0,0],[2,2,2,1,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] [10,10]=>[[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17,18,19,20]]=>[[10,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,5,0,0,0,0,0,0,0,0,0,0,0,0,0],[10,4,0,0,0,0,0,0,0,0,0,0,0,0],[10,3,0,0,0,0,0,0,0,0,0,0,0],[10,2,0,0,0,0,0,0,0,0,0,0],[10,1,0,0,0,0,0,0,0,0,0],[10,0,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] [9,9]=>[[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16,17,18]]=>[[9,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,6,0,0,0,0,0,0,0,0,0,0,0,0,0],[9,5,0,0,0,0,0,0,0,0,0,0,0,0],[9,4,0,0,0,0,0,0,0,0,0,0,0],[9,3,0,0,0,0,0,0,0,0,0,0],[9,2,0,0,0,0,0,0,0,0,0],[9,1,0,0,0,0,0,0,0,0],[9,0,0,0,0,0,0,0,0],[8,0,0,0,0,0,0,0],[7,0,0,0,0,0,0],[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
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.