Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-0Cc0007;cc-rep-1Cc0007;cc-rep-2Cc0007;cc-rep-3
[1,0]=>[[1],[2]]=>[[1,2]]=>[[1,2]] [1,0,1,0]=>[[1,3],[2,4]]=>[[1,2],[3,4]]=>[[1,2],[3,4]] [1,1,0,0]=>[[1,2],[3,4]]=>[[1,3],[2,4]]=>[[1,3],[2,4]] [1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]] [1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[[1,2],[3,5],[4,6]]=>[[1,3],[2,4],[5,6]] [1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[[1,3],[2,4],[5,6]]=>[[1,2],[3,5],[4,6]] [1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[[1,3],[2,5],[4,6]]=>[[1,3],[2,5],[4,6]] [1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]] [1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[[1,2],[3,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,6],[7,8]] [1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2],[3,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,6],[7,8]] [1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[[1,2],[3,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,6],[7,8]] [1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2],[3,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,6],[7,8]] [1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2],[3,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,6],[7,8]] [1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3],[2,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,7],[6,8]] [1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[[1,3],[2,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,7],[6,8]] [1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[[1,3],[2,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,7],[6,8]] [1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[[1,3],[2,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,7],[6,8]] [1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[[1,3],[2,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,7],[6,8]] [1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[[1,4],[2,5],[3,6],[7,8]]=>[[1,2],[3,6],[4,7],[5,8]] [1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>[[1,4],[2,5],[3,7],[6,8]]=>[[1,3],[2,6],[4,7],[5,8]] [1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>[[1,4],[2,6],[3,7],[5,8]]=>[[1,4],[2,6],[3,7],[5,8]] [1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[[1,5],[2,6],[3,7],[4,8]]=>[[1,5],[2,6],[3,7],[4,8]] [1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]] [1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,6],[7,8],[9,10]] [1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[[1,2],[3,4],[5,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,6],[7,8],[9,10]] [1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[[1,2],[3,4],[5,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,6],[7,8],[9,10]] [1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,6,7],[2,4,8,9,10]]=>[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,6],[7,8],[9,10]] [1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[[1,2],[3,5],[4,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,7],[6,8],[9,10]] [1,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,8],[2,5,6,9,10]]=>[[1,2],[3,5],[4,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,7],[6,8],[9,10]] [1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[[1,2],[3,5],[4,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,7],[6,8],[9,10]] [1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[[1,2],[3,5],[4,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,7],[6,8],[9,10]] [1,0,1,1,0,1,1,0,0,0]=>[[1,3,4,6,7],[2,5,8,9,10]]=>[[1,2],[3,5],[4,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,7],[6,8],[9,10]] [1,0,1,1,1,0,0,0,1,0]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[[1,2],[3,6],[4,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,7],[5,8],[9,10]] [1,0,1,1,1,0,0,1,0,0]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[[1,2],[3,6],[4,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,7],[5,8],[9,10]] [1,0,1,1,1,0,1,0,0,0]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[[1,2],[3,6],[4,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,7],[5,8],[9,10]] [1,0,1,1,1,1,0,0,0,0]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,7],[4,8],[9,10]] [1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,9],[8,10]] [1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[[1,3],[2,4],[5,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,6],[7,9],[8,10]] [1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,9],[3,4,7,8,10]]=>[[1,3],[2,4],[5,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,6],[7,9],[8,10]] [1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[[1,3],[2,4],[5,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,6],[7,9],[8,10]] [1,1,0,0,1,1,1,0,0,0]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,3],[2,4],[5,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,6],[7,9],[8,10]] [1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,7],[6,9],[8,10]] [1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[[1,3],[2,5],[4,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,7],[6,9],[8,10]] [1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[[1,3],[2,5],[4,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,7],[6,9],[8,10]] [1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,7],[6,9],[8,10]] [1,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[[1,3],[2,5],[4,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,7],[6,9],[8,10]] [1,1,0,1,1,0,0,0,1,0]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[[1,3],[2,6],[4,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,7],[5,9],[8,10]] [1,1,0,1,1,0,0,1,0,0]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,3],[2,6],[4,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,7],[5,9],[8,10]] [1,1,0,1,1,0,1,0,0,0]=>[[1,2,4,5,7],[3,6,8,9,10]]=>[[1,3],[2,6],[4,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,7],[5,9],[8,10]] [1,1,0,1,1,1,0,0,0,0]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[[1,3],[2,7],[4,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,7],[4,9],[8,10]] [1,1,1,0,0,0,1,0,1,0]=>[[1,2,3,7,9],[4,5,6,8,10]]=>[[1,4],[2,5],[3,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,8],[6,9],[7,10]] [1,1,1,0,0,0,1,1,0,0]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,4],[2,5],[3,6],[7,9],[8,10]]=>[[1,3],[2,4],[5,8],[6,9],[7,10]] [1,1,1,0,0,1,0,0,1,0]=>[[1,2,3,6,9],[4,5,7,8,10]]=>[[1,4],[2,5],[3,7],[6,8],[9,10]]=>[[1,2],[3,5],[4,8],[6,9],[7,10]] [1,1,1,0,0,1,0,1,0,0]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[[1,4],[2,5],[3,7],[6,9],[8,10]]=>[[1,3],[2,5],[4,8],[6,9],[7,10]] [1,1,1,0,0,1,1,0,0,0]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[[1,4],[2,5],[3,8],[6,9],[7,10]]=>[[1,4],[2,5],[3,8],[6,9],[7,10]] [1,1,1,0,1,0,0,0,1,0]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[[1,4],[2,6],[3,7],[5,8],[9,10]]=>[[1,2],[3,6],[4,8],[5,9],[7,10]] [1,1,1,0,1,0,0,1,0,0]=>[[1,2,3,5,8],[4,6,7,9,10]]=>[[1,4],[2,6],[3,7],[5,9],[8,10]]=>[[1,3],[2,6],[4,8],[5,9],[7,10]] [1,1,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7],[4,6,8,9,10]]=>[[1,4],[2,6],[3,8],[5,9],[7,10]]=>[[1,4],[2,6],[3,8],[5,9],[7,10]] [1,1,1,0,1,1,0,0,0,0]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[[1,4],[2,7],[3,8],[5,9],[6,10]]=>[[1,5],[2,6],[3,8],[4,9],[7,10]] [1,1,1,1,0,0,0,0,1,0]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,5],[2,6],[3,7],[4,8],[9,10]]=>[[1,2],[3,7],[4,8],[5,9],[6,10]] [1,1,1,1,0,0,0,1,0,0]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,5],[2,6],[3,7],[4,9],[8,10]]=>[[1,3],[2,7],[4,8],[5,9],[6,10]] [1,1,1,1,0,0,1,0,0,0]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,5],[2,6],[3,8],[4,9],[7,10]]=>[[1,4],[2,7],[3,8],[5,9],[6,10]] [1,1,1,1,0,1,0,0,0,0]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,5],[2,7],[3,8],[4,9],[6,10]]=>[[1,5],[2,7],[3,8],[4,9],[6,10]] [1,1,1,1,1,0,0,0,0,0]=>[[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]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[[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]]
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second 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.