Identifier
Mp00042:
Integer partitions
—initial tableau⟶
Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Images
=>
Cc0002;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-2
[1]=>[[1]]=>[[1]]
[2]=>[[1,2]]=>[[1,2]]
[1,1]=>[[1],[2]]=>[[1],[2]]
[3]=>[[1,2,3]]=>[[1,2,3]]
[2,1]=>[[1,2],[3]]=>[[1,3],[2]]
[1,1,1]=>[[1],[2],[3]]=>[[1],[2],[3]]
[4]=>[[1,2,3,4]]=>[[1,2,3,4]]
[3,1]=>[[1,2,3],[4]]=>[[1,3,4],[2]]
[2,2]=>[[1,2],[3,4]]=>[[1,2],[3,4]]
[2,1,1]=>[[1,2],[3],[4]]=>[[1,4],[2],[3]]
[1,1,1,1]=>[[1],[2],[3],[4]]=>[[1],[2],[3],[4]]
[5]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]]
[4,1]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]
[3,2]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]
[3,1,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]
[2,2,1]=>[[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]
[2,1,1,1]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]
[1,1,1,1,1]=>[[1],[2],[3],[4],[5]]=>[[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]]=>[[1,3,4,5,6],[2]]
[4,2]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]
[4,1,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]
[3,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]
[3,2,1]=>[[1,2,3],[4,5],[6]]=>[[1,3,6],[2,5],[4]]
[3,1,1,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]
[2,2,2]=>[[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]]
[2,2,1,1]=>[[1,2],[3,4],[5],[6]]=>[[1,4],[2,6],[3],[5]]
[2,1,1,1,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]
[1,1,1,1,1,1]=>[[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]]
[6,1]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]
[5,2]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]
[5,1,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]
[4,3]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]
[4,2,1]=>[[1,2,3,4],[5,6],[7]]=>[[1,3,6,7],[2,5],[4]]
[4,1,1,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]
[3,3,1]=>[[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]
[3,2,2]=>[[1,2,3],[4,5],[6,7]]=>[[1,2,7],[3,4],[5,6]]
[3,2,1,1]=>[[1,2,3],[4,5],[6],[7]]=>[[1,4,7],[2,6],[3],[5]]
[3,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]
[2,2,2,1]=>[[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]
[2,2,1,1,1]=>[[1,2],[3,4],[5],[6],[7]]=>[[1,5],[2,7],[3],[4],[6]]
[2,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]
[1,1,1,1,1,1,1]=>[[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]]
[7,1]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]
[6,2]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]
[6,1,1]=>[[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]
[5,3]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]
[5,2,1]=>[[1,2,3,4,5],[6,7],[8]]=>[[1,3,6,7,8],[2,5],[4]]
[5,1,1,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]
[4,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]
[4,3,1]=>[[1,2,3,4],[5,6,7],[8]]=>[[1,3,4,8],[2,6,7],[5]]
[4,2,2]=>[[1,2,3,4],[5,6],[7,8]]=>[[1,2,7,8],[3,4],[5,6]]
[4,2,1,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[[1,4,7,8],[2,6],[3],[5]]
[4,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]
[3,3,2]=>[[1,2,3],[4,5,6],[7,8]]=>[[1,2,5],[3,4,8],[6,7]]
[3,3,1,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[[1,4,5],[2,7,8],[3],[6]]
[3,2,2,1]=>[[1,2,3],[4,5],[6,7],[8]]=>[[1,3,8],[2,5],[4,7],[6]]
[3,2,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8]]=>[[1,5,8],[2,7],[3],[4],[6]]
[3,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]
[2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,6],[7,8]]
[2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[1,4],[2,6],[3,8],[5],[7]]
[2,2,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]
[2,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[1,1,1,1,1,1,1,1]=>[[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]]
[8,1]=>[[1,2,3,4,5,6,7,8],[9]]=>[[1,3,4,5,6,7,8,9],[2]]
[7,2]=>[[1,2,3,4,5,6,7],[8,9]]=>[[1,2,5,6,7,8,9],[3,4]]
[7,1,1]=>[[1,2,3,4,5,6,7],[8],[9]]=>[[1,4,5,6,7,8,9],[2],[3]]
[6,3]=>[[1,2,3,4,5,6],[7,8,9]]=>[[1,2,3,7,8,9],[4,5,6]]
[6,2,1]=>[[1,2,3,4,5,6],[7,8],[9]]=>[[1,3,6,7,8,9],[2,5],[4]]
[6,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[[1,5,6,7,8,9],[2],[3],[4]]
[5,4]=>[[1,2,3,4,5],[6,7,8,9]]=>[[1,2,3,4,9],[5,6,7,8]]
[5,3,1]=>[[1,2,3,4,5],[6,7,8],[9]]=>[[1,3,4,8,9],[2,6,7],[5]]
[5,2,2]=>[[1,2,3,4,5],[6,7],[8,9]]=>[[1,2,7,8,9],[3,4],[5,6]]
[5,2,1,1]=>[[1,2,3,4,5],[6,7],[8],[9]]=>[[1,4,7,8,9],[2,6],[3],[5]]
[5,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[[1,6,7,8,9],[2],[3],[4],[5]]
[4,4,1]=>[[1,2,3,4],[5,6,7,8],[9]]=>[[1,3,4,5],[2,7,8,9],[6]]
[4,3,2]=>[[1,2,3,4],[5,6,7],[8,9]]=>[[1,2,5,9],[3,4,8],[6,7]]
[4,3,1,1]=>[[1,2,3,4],[5,6,7],[8],[9]]=>[[1,4,5,9],[2,7,8],[3],[6]]
[4,2,2,1]=>[[1,2,3,4],[5,6],[7,8],[9]]=>[[1,3,8,9],[2,5],[4,7],[6]]
[4,2,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9]]=>[[1,5,8,9],[2,7],[3],[4],[6]]
[4,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[[1,7,8,9],[2],[3],[4],[5],[6]]
[3,3,3]=>[[1,2,3],[4,5,6],[7,8,9]]=>[[1,2,3],[4,5,6],[7,8,9]]
[3,3,2,1]=>[[1,2,3],[4,5,6],[7,8],[9]]=>[[1,3,6],[2,5,9],[4,8],[7]]
[3,3,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9]]=>[[1,5,6],[2,8,9],[3],[4],[7]]
[3,2,2,2]=>[[1,2,3],[4,5],[6,7],[8,9]]=>[[1,2,9],[3,4],[5,6],[7,8]]
[3,2,2,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9]]=>[[1,4,9],[2,6],[3,8],[5],[7]]
[3,2,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9]]=>[[1,6,9],[2,8],[3],[4],[5],[7]]
[3,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[2,2,2,2,1]=>[[1,2],[3,4],[5,6],[7,8],[9]]=>[[1,3],[2,5],[4,7],[6,9],[8]]
[2,2,2,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9]]=>[[1,5],[2,7],[3,9],[4],[6],[8]]
[2,2,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]
[2,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[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]]
[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]]=>[[1,3,4,5,6,7,8,9,10],[2]]
[8,2]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[[1,2,5,6,7,8,9,10],[3,4]]
[8,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[7,3]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[[1,2,3,7,8,9,10],[4,5,6]]
[7,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10]]=>[[1,3,6,7,8,9,10],[2,5],[4]]
[7,1,1,1]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[6,4]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[[1,2,3,4,9,10],[5,6,7,8]]
[6,3,1]=>[[1,2,3,4,5,6],[7,8,9],[10]]=>[[1,3,4,8,9,10],[2,6,7],[5]]
[6,2,2]=>[[1,2,3,4,5,6],[7,8],[9,10]]=>[[1,2,7,8,9,10],[3,4],[5,6]]
[6,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9],[10]]=>[[1,4,7,8,9,10],[2,6],[3],[5]]
[6,1,1,1,1]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]
[5,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,2,3,4,5],[6,7,8,9,10]]
[5,4,1]=>[[1,2,3,4,5],[6,7,8,9],[10]]=>[[1,3,4,5,10],[2,7,8,9],[6]]
[5,3,2]=>[[1,2,3,4,5],[6,7,8],[9,10]]=>[[1,2,5,9,10],[3,4,8],[6,7]]
[5,3,1,1]=>[[1,2,3,4,5],[6,7,8],[9],[10]]=>[[1,4,5,9,10],[2,7,8],[3],[6]]
[5,2,2,1]=>[[1,2,3,4,5],[6,7],[8,9],[10]]=>[[1,3,8,9,10],[2,5],[4,7],[6]]
[5,2,1,1,1]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]
[5,1,1,1,1,1]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[4,4,2]=>[[1,2,3,4],[5,6,7,8],[9,10]]=>[[1,2,5,6],[3,4,9,10],[7,8]]
[4,4,1,1]=>[[1,2,3,4],[5,6,7,8],[9],[10]]=>[[1,4,5,6],[2,8,9,10],[3],[7]]
[4,3,3]=>[[1,2,3,4],[5,6,7],[8,9,10]]=>[[1,2,3,10],[4,5,6],[7,8,9]]
[4,3,2,1]=>[[1,2,3,4],[5,6,7],[8,9],[10]]=>[[1,3,6,10],[2,5,9],[4,8],[7]]
[4,3,1,1,1]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[[1,5,6,10],[2,8,9],[3],[4],[7]]
[4,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10]]=>[[1,2,9,10],[3,4],[5,6],[7,8]]
[4,2,2,1,1]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[[1,4,9,10],[2,6],[3,8],[5],[7]]
[4,2,1,1,1,1]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[[1,6,9,10],[2,8],[3],[4],[5],[7]]
[4,1,1,1,1,1,1]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]
[3,3,3,1]=>[[1,2,3],[4,5,6],[7,8,9],[10]]=>[[1,3,4],[2,6,7],[5,9,10],[8]]
[3,3,2,2]=>[[1,2,3],[4,5,6],[7,8],[9,10]]=>[[1,2,7],[3,4,10],[5,6],[8,9]]
[3,3,2,1,1]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[[1,4,7],[2,6,10],[3,9],[5],[8]]
[3,3,1,1,1,1]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[[1,6,7],[2,9,10],[3],[4],[5],[8]]
[3,2,2,2,1]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]
[3,2,2,1,1,1]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[[1,5,10],[2,7],[3,9],[4],[6],[8]]
[3,2,1,1,1,1,1]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[[1,7,10],[2,9],[3],[4],[5],[6],[8]]
[3,1,1,1,1,1,1,1]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]
[2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]
[2,2,2,2,1,1]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[[1,4],[2,6],[3,8],[5,10],[7],[9]]
[2,2,2,1,1,1,1]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]]
[2,2,1,1,1,1,1,1]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]
[2,1,1,1,1,1,1,1,1]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[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]]
[10,1]=>[[1,2,3,4,5,6,7,8,9,10],[11]]=>[[1,3,4,5,6,7,8,9,10,11],[2]]
[9,2]=>[[1,2,3,4,5,6,7,8,9],[10,11]]=>[[1,2,5,6,7,8,9,10,11],[3,4]]
[9,1,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11]]=>[[1,4,5,6,7,8,9,10,11],[2],[3]]
[8,3]=>[[1,2,3,4,5,6,7,8],[9,10,11]]=>[[1,2,3,7,8,9,10,11],[4,5,6]]
[8,2,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11]]=>[[1,3,6,7,8,9,10,11],[2,5],[4]]
[8,1,1,1]=>[[1,2,3,4,5,6,7,8],[9],[10],[11]]=>[[1,5,6,7,8,9,10,11],[2],[3],[4]]
[7,3,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11]]=>[[1,3,4,8,9,10,11],[2,6,7],[5]]
[7,2,2]=>[[1,2,3,4,5,6,7],[8,9],[10,11]]=>[[1,2,7,8,9,10,11],[3,4],[5,6]]
[7,2,1,1]=>[[1,2,3,4,5,6,7],[8,9],[10],[11]]=>[[1,4,7,8,9,10,11],[2,6],[3],[5]]
[6,3,2]=>[[1,2,3,4,5,6],[7,8,9],[10,11]]=>[[1,2,5,9,10,11],[3,4,8],[6,7]]
[6,3,1,1]=>[[1,2,3,4,5,6],[7,8,9],[10],[11]]=>[[1,4,5,9,10,11],[2,7,8],[3],[6]]
[6,2,2,1]=>[[1,2,3,4,5,6],[7,8],[9,10],[11]]=>[[1,3,8,9,10,11],[2,5],[4,7],[6]]
[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]]
[11,1]=>[[1,2,3,4,5,6,7,8,9,10,11],[12]]=>[[1,3,4,5,6,7,8,9,10,11,12],[2]]
[10,2]=>[[1,2,3,4,5,6,7,8,9,10],[11,12]]=>[[1,2,5,6,7,8,9,10,11,12],[3,4]]
[9,3]=>[[1,2,3,4,5,6,7,8,9],[10,11,12]]=>[[1,2,3,7,8,9,10,11,12],[4,5,6]]
[9,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12]]=>[[1,3,6,7,8,9,10,11,12],[2,5],[4]]
[9,1,1,1]=>[[1,2,3,4,5,6,7,8,9],[10],[11],[12]]=>[[1,5,6,7,8,9,10,11,12],[2],[3],[4]]
[8,3,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12]]=>[[1,3,4,8,9,10,11,12],[2,6,7],[5]]
[8,2,2]=>[[1,2,3,4,5,6,7,8],[9,10],[11,12]]=>[[1,2,7,8,9,10,11,12],[3,4],[5,6]]
[8,2,1,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11],[12]]=>[[1,4,7,8,9,10,11,12],[2,6],[3],[5]]
[7,3,2]=>[[1,2,3,4,5,6,7],[8,9,10],[11,12]]=>[[1,2,5,9,10,11,12],[3,4,8],[6,7]]
[7,3,1,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11],[12]]=>[[1,4,5,9,10,11,12],[2,7,8],[3],[6]]
[7,2,2,1]=>[[1,2,3,4,5,6,7],[8,9],[10,11],[12]]=>[[1,3,8,9,10,11,12],[2,5],[4,7],[6]]
[6,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]
[6,3,2,1]=>[[1,2,3,4,5,6],[7,8,9],[10,11],[12]]=>[[1,3,6,10,11,12],[2,5,9],[4,8],[7]]
[6,2,2,1,1]=>[[1,2,3,4,5,6],[7,8],[9,10],[11],[12]]=>[[1,4,9,10,11,12],[2,6],[3,8],[5],[7]]
[4,2,2,2,2]=>[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2,11,12],[3,4],[5,6],[7,8],[9,10]]
[2,2,2,2,2,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]
[1,1,1,1,1,1,1,1,1,1,1,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[9,3,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13]]=>[[1,3,4,8,9,10,11,12,13],[2,6,7],[5]]
[9,2,2]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12,13]]=>[[1,2,7,8,9,10,11,12,13],[3,4],[5,6]]
[9,2,1,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12],[13]]=>[[1,4,7,8,9,10,11,12,13],[2,6],[3],[5]]
[8,3,2]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12,13]]=>[[1,2,5,9,10,11,12,13],[3,4,8],[6,7]]
[8,3,1,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12],[13]]=>[[1,4,5,9,10,11,12,13],[2,7,8],[3],[6]]
[8,2,2,1]=>[[1,2,3,4,5,6,7,8],[9,10],[11,12],[13]]=>[[1,3,8,9,10,11,12,13],[2,5],[4,7],[6]]
[7,3,2,1]=>[[1,2,3,4,5,6,7],[8,9,10],[11,12],[13]]=>[[1,3,6,10,11,12,13],[2,5,9],[4,8],[7]]
[9,3,2]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13,14]]=>[[1,2,5,9,10,11,12,13,14],[3,4,8],[6,7]]
[9,3,1,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13],[14]]=>[[1,4,5,9,10,11,12,13,14],[2,7,8],[3],[6]]
[9,2,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11],[12,13],[14]]=>[[1,3,8,9,10,11,12,13,14],[2,5],[4,7],[6]]
[8,3,2,1]=>[[1,2,3,4,5,6,7,8],[9,10,11],[12,13],[14]]=>[[1,3,6,10,11,12,13,14],[2,5,9],[4,8],[7]]
[9,3,2,1]=>[[1,2,3,4,5,6,7,8,9],[10,11,12],[13,14],[15]]=>[[1,3,6,10,11,12,13,14,15],[2,5,9],[4,8],[7]]
[]=>[]=>[]
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
searching the database
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