Identifier
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00226: Standard tableaux —row-to-column-descents⟶ Standard tableaux
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0007;cc-rep-2Cc0007;cc-rep-3
[1,0]=>[1,0]=>[[1],[2]]=>[[1],[2]] [1,0,1,0]=>[1,1,0,0]=>[[1,2],[3,4]]=>[[1,3],[2,4]] [1,1,0,0]=>[1,0,1,0]=>[[1,3],[2,4]]=>[[1,2],[3,4]] [1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[[1,3,5],[2,4,6]] [1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]] [1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]] [1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[[1,2,3],[4,5,6]] [1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[[1,2,4],[3,5,6]] [1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[[1,3,5,7],[2,4,6,8]] [1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[[1,3,5,6],[2,4,7,8]] [1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[[1,3,4,7],[2,5,6,8]] [1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>[[1,3,4,5],[2,6,7,8]] [1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[[1,3,4,6],[2,5,7,8]] [1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>[[1,2,5,7],[3,4,6,8]] [1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[[1,2,5,6],[3,4,7,8]] [1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[[1,2,3,7],[4,5,6,8]] [1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>[[1,2,3,4],[5,6,7,8]] [1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[[1,2,3,6],[4,5,7,8]] [1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[[1,2,4,7],[3,5,6,8]] [1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>[[1,2,4,5],[3,6,7,8]] [1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[[1,2,3,5],[4,6,7,8]] [1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[[1,2,4,6],[3,5,7,8]] [1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[[1,3,5,7,9],[2,4,6,8,10]] [1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[[1,3,5,7,8],[2,4,6,9,10]] [1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[[1,3,5,6,9],[2,4,7,8,10]] [1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[[1,3,5,6,7],[2,4,8,9,10]] [1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[[1,2,3,7,9],[4,5,6,8,10]]=>[[1,3,5,6,8],[2,4,7,9,10]] [1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[[1,3,4,7,9],[2,5,6,8,10]] [1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[[1,2,5,6,9],[3,4,7,8,10]]=>[[1,3,4,7,8],[2,5,6,9,10]] [1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[[1,3,4,5,9],[2,6,7,8,10]] [1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[[1,3,4,5,6],[2,7,8,9,10]] [1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[[1,2,3,6,9],[4,5,7,8,10]]=>[[1,3,4,5,8],[2,6,7,9,10]] [1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[[1,3,4,6,9],[2,5,7,8,10]] [1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[[1,3,4,6,7],[2,5,8,9,10]] [1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[[1,3,4,5,7],[2,6,8,9,10]] [1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[[1,3,4,6,8],[2,5,7,9,10]] [1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[[1,2,5,7,9],[3,4,6,8,10]] [1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[[1,2,5,7,8],[3,4,6,9,10]] [1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[[1,3,4,7,8],[2,5,6,9,10]]=>[[1,2,5,6,9],[3,4,7,8,10]] [1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[[1,2,5,6,7],[3,4,8,9,10]] [1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[[1,2,5,6,8],[3,4,7,9,10]] [1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[[1,2,3,7,9],[4,5,6,8,10]] [1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[[1,2,3,7,8],[4,5,6,9,10]] [1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[[1,2,3,4,9],[5,6,7,8,10]] [1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[[1,2,3,4,5],[6,7,8,9,10]] [1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[[1,2,3,4,8],[5,6,7,9,10]] [1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[[1,2,3,6,9],[4,5,7,8,10]] [1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[[1,2,4,5,8],[3,6,7,9,10]]=>[[1,2,3,6,7],[4,5,8,9,10]] [1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[[1,2,3,5,8],[4,6,7,9,10]]=>[[1,2,3,4,7],[5,6,8,9,10]] [1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[[1,2,3,6,8],[4,5,7,9,10]] [1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,6,7],[2,4,8,9,10]]=>[[1,2,4,7,9],[3,5,6,8,10]] [1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[[1,2,4,7,8],[3,5,6,9,10]] [1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[1,3,4,6,7],[2,5,8,9,10]]=>[[1,2,4,5,9],[3,6,7,8,10]] [1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[[1,2,4,5,6],[3,7,8,9,10]] [1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[[1,2,4,5,8],[3,6,7,9,10]] [1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[[1,2,3,5,9],[4,6,7,8,10]] [1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[[1,2,4,5,7],[3,6,8,9,10]]=>[[1,2,3,5,6],[4,7,8,9,10]] [1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7],[4,6,8,9,10]]=>[[1,2,3,4,6],[5,7,8,9,10]] [1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[[1,2,3,5,8],[4,6,7,9,10]] [1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[[1,2,4,6,9],[3,5,7,8,10]] [1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[[1,2,4,6,7],[3,5,8,9,10]] [1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[[1,2,4,5,7],[3,6,8,9,10]] [1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[[1,2,3,5,7],[4,6,8,9,10]] [1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[[1,2,4,6,8],[3,5,7,9,10]] [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]] [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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
row-to-column-descents
Description
Return a standard tableau whose column descent set equals the row descent set of the original tableau.
A column descent in a standard tableau is an entry $i$ such that $i+1$ appears in a column to the left of the cell containing $i$, in English notation.
A row descent is an entry $i$ such that $i+1$ appears in a row above of the cell containing $i$.