Identifier
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-2Cc0007;cc-rep-3
[1]=>[[1]]=>[[1]]=>[[1]] [2]=>[[1,2]]=>[[1],[2]]=>[[1],[2]] [1,1]=>[[1],[2]]=>[[1,2]]=>[[1,2]] [3]=>[[1,2,3]]=>[[1],[2],[3]]=>[[1],[2],[3]] [2,1]=>[[1,2],[3]]=>[[1,3],[2]]=>[[1,2],[3]] [1,1,1]=>[[1],[2],[3]]=>[[1,2,3]]=>[[1,2,3]] [4]=>[[1,2,3,4]]=>[[1],[2],[3],[4]]=>[[1],[2],[3],[4]] [3,1]=>[[1,2,3],[4]]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]] [2,2]=>[[1,2],[3,4]]=>[[1,3],[2,4]]=>[[1,3],[2,4]] [2,1,1]=>[[1,2],[3],[4]]=>[[1,3,4],[2]]=>[[1,2,3],[4]] [1,1,1,1]=>[[1],[2],[3],[4]]=>[[1,2,3,4]]=>[[1,2,3,4]] [5]=>[[1,2,3,4,5]]=>[[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]] [4,1]=>[[1,2,3,4],[5]]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]] [3,2]=>[[1,2,3],[4,5]]=>[[1,4],[2,5],[3]]=>[[1,3],[2,4],[5]] [3,1,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]] [2,2,1]=>[[1,2],[3,4],[5]]=>[[1,3,5],[2,4]]=>[[1,2,4],[3,5]] [2,1,1,1]=>[[1,2],[3],[4],[5]]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]] [1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]] [6]=>[[1,2,3,4,5,6]]=>[[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]] [5,1]=>[[1,2,3,4,5],[6]]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]] [4,2]=>[[1,2,3,4],[5,6]]=>[[1,5],[2,6],[3],[4]]=>[[1,3],[2,4],[5],[6]] [4,1,1]=>[[1,2,3,4],[5],[6]]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]] [3,3]=>[[1,2,3],[4,5,6]]=>[[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]] [3,2,1]=>[[1,2,3],[4,5],[6]]=>[[1,4,6],[2,5],[3]]=>[[1,2,4],[3,5],[6]] [3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]] [2,2,2]=>[[1,2],[3,4],[5,6]]=>[[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]] [2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]] [2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]] [1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6]]=>[[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]] [7]=>[[1,2,3,4,5,6,7]]=>[[1],[2],[3],[4],[5],[6],[7]]=>[[1],[2],[3],[4],[5],[6],[7]] [6,1]=>[[1,2,3,4,5,6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]] [5,2]=>[[1,2,3,4,5],[6,7]]=>[[1,6],[2,7],[3],[4],[5]]=>[[1,3],[2,4],[5],[6],[7]] [5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]] [4,3]=>[[1,2,3,4],[5,6,7]]=>[[1,5],[2,6],[3,7],[4]]=>[[1,4],[2,5],[3,6],[7]] [4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[[1,5,7],[2,6],[3],[4]]=>[[1,2,4],[3,5],[6],[7]] [4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]] [3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]] [3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[[1,4,6],[2,5,7],[3]]=>[[1,3,5],[2,4,6],[7]] [3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[[1,4,6,7],[2,5],[3]]=>[[1,2,3,5],[4,6],[7]] [3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]] [2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]] [2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]] [2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]] [1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]] [8]=>[[1,2,3,4,5,6,7,8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]] [7,1]=>[[1,2,3,4,5,6,7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]] [6,2]=>[[1,2,3,4,5,6],[7,8]]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[[1,3],[2,4],[5],[6],[7],[8]] [6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]] [5,3]=>[[1,2,3,4,5],[6,7,8]]=>[[1,6],[2,7],[3,8],[4],[5]]=>[[1,4],[2,5],[3,6],[7],[8]] [5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,4],[3,5],[6],[7],[8]] [5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]] [4,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,5],[2,6],[3,7],[4,8]]=>[[1,5],[2,6],[3,7],[4,8]] [4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]=>[[1,2,5],[3,6],[4,7],[8]] [4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[[1,5,7],[2,6,8],[3],[4]]=>[[1,3,5],[2,4,6],[7],[8]] [4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]=>[[1,2,3,5],[4,6],[7],[8]] [4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]] [3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[[1,4,7],[2,5,8],[3,6]]=>[[1,3,6],[2,4,7],[5,8]] [3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[[1,4,7,8],[2,5],[3,6]]=>[[1,2,3,6],[4,7],[5,8]] [3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]=>[[1,2,4,6],[3,5,7],[8]] [3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[[1,4,6,7,8],[2,5],[3]]=>[[1,2,3,4,6],[5,7],[8]] [3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]] [2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]] [2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[1,3,5,7,8],[2,4,6]]=>[[1,2,3,5,7],[4,6,8]] [2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,3,5,6,7,8],[2,4]]=>[[1,2,3,4,5,7],[6,8]] [2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]] [1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]] [9]=>[[1,2,3,4,5,6,7,8,9]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]] [8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]] [7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[[1,3],[2,4],[5],[6],[7],[8],[9]] [7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7],[8],[9]] [6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,7],[2,8],[3,9],[4],[5],[6]]=>[[1,4],[2,5],[3,6],[7],[8],[9]] [6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[1,7,9],[2,8],[3],[4],[5],[6]]=>[[1,2,4],[3,5],[6],[7],[8],[9]] [6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[[1,2,3,4],[5],[6],[7],[8],[9]] [5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,6],[2,7],[3,8],[4,9],[5]]=>[[1,5],[2,6],[3,7],[4,8],[9]] [5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[[1,6,9],[2,7],[3,8],[4],[5]]=>[[1,2,5],[3,6],[4,7],[8],[9]] [5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[1,6,8],[2,7,9],[3],[4],[5]]=>[[1,3,5],[2,4,6],[7],[8],[9]] [5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[1,6,8,9],[2,7],[3],[4],[5]]=>[[1,2,3,5],[4,6],[7],[8],[9]] [5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[[1,2,3,4,5],[6],[7],[8],[9]] [4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[[1,5,9],[2,6],[3,7],[4,8]]=>[[1,2,6],[3,7],[4,8],[5,9]] [4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[[1,5,8],[2,6,9],[3,7],[4]]=>[[1,3,6],[2,4,7],[5,8],[9]] [4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[[1,5,8,9],[2,6],[3,7],[4]]=>[[1,2,3,6],[4,7],[5,8],[9]] [4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[1,5,7,9],[2,6,8],[3],[4]]=>[[1,2,4,6],[3,5,7],[8],[9]] [4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[1,5,7,8,9],[2,6],[3],[4]]=>[[1,2,3,4,6],[5,7],[8],[9]] [4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[[1,2,3,4,5,6],[7],[8],[9]] [3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[[1,4,7],[2,5,8],[3,6,9]]=>[[1,4,7],[2,5,8],[3,6,9]] [3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[[1,4,7,9],[2,5,8],[3,6]]=>[[1,2,4,7],[3,5,8],[6,9]] [3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[[1,4,7,8,9],[2,5],[3,6]]=>[[1,2,3,4,7],[5,8],[6,9]] [3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[[1,4,6,8],[2,5,7,9],[3]]=>[[1,3,5,7],[2,4,6,8],[9]] [3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[[1,4,6,8,9],[2,5,7],[3]]=>[[1,2,3,5,7],[4,6,8],[9]] [3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[[1,4,6,7,8,9],[2,5],[3]]=>[[1,2,3,4,5,7],[6,8],[9]] [3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]=>[[1,2,3,4,5,6,7],[8],[9]] [2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,3,5,7,9],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7,9]] [2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[[1,3,5,7,8,9],[2,4,6]]=>[[1,2,3,4,6,8],[5,7,9]] [2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[[1,3,5,6,7,8,9],[2,4]]=>[[1,2,3,4,5,6,8],[7,9]] [2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]=>[[1,2,3,4,5,6,7,8],[9]] [1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2,3,4,5,6,7,8,9]]=>[[1,2,3,4,5,6,7,8,9]] [10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [9,1]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] [8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] [8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] [7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]] [7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7],[8],[9],[10]] [7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]] [6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,7],[2,8],[3,9],[4,10],[5],[6]]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]] [6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[1,7,10],[2,8],[3,9],[4],[5],[6]]=>[[1,2,5],[3,6],[4,7],[8],[9],[10]] [6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[1,7,9],[2,8,10],[3],[4],[5],[6]]=>[[1,3,5],[2,4,6],[7],[8],[9],[10]] [6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[1,7,9,10],[2,8],[3],[4],[5],[6]]=>[[1,2,3,5],[4,6],[7],[8],[9],[10]] [6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]] [5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[[1,6],[2,7],[3,8],[4,9],[5,10]] [5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[[1,6,10],[2,7],[3,8],[4,9],[5]]=>[[1,2,6],[3,7],[4,8],[5,9],[10]] [5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[[1,6,9],[2,7,10],[3,8],[4],[5]]=>[[1,3,6],[2,4,7],[5,8],[9],[10]] [5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[[1,6,9,10],[2,7],[3,8],[4],[5]]=>[[1,2,3,6],[4,7],[5,8],[9],[10]] [5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[1,6,8,10],[2,7,9],[3],[4],[5]]=>[[1,2,4,6],[3,5,7],[8],[9],[10]] [5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[1,6,8,9,10],[2,7],[3],[4],[5]]=>[[1,2,3,4,6],[5,7],[8],[9],[10]] [5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[[1,2,3,4,5,6],[7],[8],[9],[10]] [4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[[1,5,9],[2,6,10],[3,7],[4,8]]=>[[1,3,7],[2,4,8],[5,9],[6,10]] [4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[[1,5,9,10],[2,6],[3,7],[4,8]]=>[[1,2,3,7],[4,8],[5,9],[6,10]] [4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[[1,5,8],[2,6,9],[3,7,10],[4]]=>[[1,4,7],[2,5,8],[3,6,9],[10]] [4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[[1,5,8,10],[2,6,9],[3,7],[4]]=>[[1,2,4,7],[3,5,8],[6,9],[10]] [4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[[1,5,8,9,10],[2,6],[3,7],[4]]=>[[1,2,3,4,7],[5,8],[6,9],[10]] [4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[1,5,7,9],[2,6,8,10],[3],[4]]=>[[1,3,5,7],[2,4,6,8],[9],[10]] [4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[1,5,7,9,10],[2,6,8],[3],[4]]=>[[1,2,3,5,7],[4,6,8],[9],[10]] [4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[1,5,7,8,9,10],[2,6],[3],[4]]=>[[1,2,3,4,5,7],[6,8],[9],[10]] [4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[[1,2,3,4,5,6,7],[8],[9],[10]] [3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[1,4,7,10],[2,5,8],[3,6,9]]=>[[1,2,5,8],[3,6,9],[4,7,10]] [3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[[1,4,7,9],[2,5,8,10],[3,6]]=>[[1,3,5,8],[2,4,6,9],[7,10]] [3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[[1,4,7,9,10],[2,5,8],[3,6]]=>[[1,2,3,5,8],[4,6,9],[7,10]] [3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[[1,4,7,8,9,10],[2,5],[3,6]]=>[[1,2,3,4,5,8],[6,9],[7,10]] [3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[[1,4,6,8,10],[2,5,7,9],[3]]=>[[1,2,4,6,8],[3,5,7,9],[10]] [3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[[1,4,6,8,9,10],[2,5,7],[3]]=>[[1,2,3,4,6,8],[5,7,9],[10]] [3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[[1,4,6,7,8,9,10],[2,5],[3]]=>[[1,2,3,4,5,6,8],[7,9],[10]] [3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[[1,2,3,4,5,6,7,8],[9],[10]] [2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]] [2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[[1,3,5,7,9,10],[2,4,6,8]]=>[[1,2,3,5,7,9],[4,6,8,10]] [2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[[1,3,5,7,8,9,10],[2,4,6]]=>[[1,2,3,4,5,7,9],[6,8,10]] [2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[[1,3,5,6,7,8,9,10],[2,4]]=>[[1,2,3,4,5,6,7,9],[8,10]] [2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[[1,2,3,4,5,6,7,8,9],[10]] [1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,2,3,4,5,6,7,8,9,10]]=>[[1,2,3,4,5,6,7,8,9,10]] [2,1,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]=>[[1,2,3,4,5,6,7,8,9,10],[11]] [12]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] [6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] [4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,5,7,9,11],[2,6,8,10,12],[3],[4]]=>[[1,3,5,7,9],[2,4,6,8,10],[11],[12]] [2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]] [1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[[1,2,3,4,5,6,7,8,9,10,11,12]] []=>[]=>[]=>[]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
conjugate
Description
Sends a standard tableau to its conjugate tableau.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.