Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0007;cc-rep-2
[1,0]=>[1,0]=>[[1],[2]]=>[1,1]
[1,0,1,0]=>[1,0,1,0]=>[[1,3],[2,4]]=>[1,2,1]
[1,1,0,0]=>[1,1,0,0]=>[[1,2],[3,4]]=>[2,2]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[[1,3,5],[2,4,6]]=>[1,2,2,1]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[[1,2,5],[3,4,6]]=>[2,3,1]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[[1,3,4],[2,5,6]]=>[1,3,2]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[[1,2,4],[3,5,6]]=>[2,2,2]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[[1,2,3],[4,5,6]]=>[3,3]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[[1,3,5,7],[2,4,6,8]]=>[1,2,2,2,1]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[[1,2,5,7],[3,4,6,8]]=>[2,3,2,1]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[[1,3,4,7],[2,5,6,8]]=>[1,3,3,1]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[[1,2,4,7],[3,5,6,8]]=>[2,2,3,1]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[[1,2,3,7],[4,5,6,8]]=>[3,4,1]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[[1,3,5,6],[2,4,7,8]]=>[1,2,3,2]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[[1,2,5,6],[3,4,7,8]]=>[2,4,2]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[[1,3,4,6],[2,5,7,8]]=>[1,3,2,2]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[[1,2,4,6],[3,5,7,8]]=>[2,2,2,2]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[[1,2,3,6],[4,5,7,8]]=>[3,3,2]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[[1,3,4,5],[2,6,7,8]]=>[1,4,3]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[[1,2,4,5],[3,6,7,8]]=>[2,3,3]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[[1,2,3,5],[4,6,7,8]]=>[3,2,3]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[[1,2,5,7,9],[3,4,6,8,10]]=>[2,3,2,2,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[[1,3,4,7,9],[2,5,6,8,10]]=>[1,3,3,2,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[[1,2,4,7,9],[3,5,6,8,10]]=>[2,2,3,2,1]
[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]]=>[3,4,2,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,6,9],[2,4,7,8,10]]=>[1,2,3,3,1]
[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]]=>[2,4,3,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[[1,3,4,6,9],[2,5,7,8,10]]=>[1,3,2,3,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,9],[3,5,7,8,10]]=>[2,2,2,3,1]
[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]]=>[3,3,3,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[[1,3,4,5,9],[2,6,7,8,10]]=>[1,4,4,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[[1,2,4,5,9],[3,6,7,8,10]]=>[2,3,4,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[[1,2,3,5,9],[4,6,7,8,10]]=>[3,2,4,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[[1,2,3,4,9],[5,6,7,8,10]]=>[4,5,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,8],[2,4,6,9,10]]=>[1,2,2,3,2]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[[1,2,5,7,8],[3,4,6,9,10]]=>[2,3,3,2]
[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]]=>[1,3,4,2]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[[1,2,4,7,8],[3,5,6,9,10]]=>[2,2,4,2]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[[1,2,3,7,8],[4,5,6,9,10]]=>[3,5,2]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,6,8],[2,4,7,9,10]]=>[1,2,3,2,2]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[[1,2,5,6,8],[3,4,7,9,10]]=>[2,4,2,2]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[1,3,4,6,8],[2,5,7,9,10]]=>[1,3,2,2,2]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8],[3,5,7,9,10]]=>[2,2,2,2,2]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[[1,2,3,6,8],[4,5,7,9,10]]=>[3,3,2,2]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[[1,3,4,5,8],[2,6,7,9,10]]=>[1,4,3,2]
[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]]=>[2,3,3,2]
[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]]=>[3,2,3,2]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[[1,2,3,4,8],[5,6,7,9,10]]=>[4,4,2]
[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]]=>[1,2,4,3]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[[1,2,5,6,7],[3,4,8,9,10]]=>[2,5,3]
[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]]=>[1,3,3,3]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,7],[3,5,8,9,10]]=>[2,2,3,3]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[[1,2,3,6,7],[4,5,8,9,10]]=>[3,4,3]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[1,3,4,5,7],[2,6,8,9,10]]=>[1,4,2,3]
[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]]=>[2,3,2,3]
[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]]=>[3,2,2,3]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[[1,2,3,4,7],[5,6,8,9,10]]=>[4,3,3]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[1,3,4,5,6],[2,7,8,9,10]]=>[1,5,4]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[[1,2,4,5,6],[3,7,8,9,10]]=>[2,4,4]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[[1,2,3,5,6],[4,7,8,9,10]]=>[3,3,4]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[[1,2,3,4,6],[5,7,8,9,10]]=>[4,2,4]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[1,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[2,3,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[1,3,3,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[2,2,3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[3,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[1,2,3,3,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[2,4,3,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[1,3,2,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[2,2,2,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[3,3,3,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[1,4,4,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[2,3,4,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[3,2,4,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[4,5,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[1,2,2,3,3,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[2,3,3,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[1,3,4,3,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[2,2,4,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[3,5,3,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[1,2,3,2,3,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[2,4,2,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[1,3,2,2,3,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[2,2,2,2,3,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[3,3,2,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[1,4,3,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[2,3,3,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[3,2,3,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[4,4,3,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[1,2,4,4,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[2,5,4,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[1,3,3,4,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[2,2,3,4,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[3,4,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[1,4,2,4,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[2,3,2,4,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[3,2,2,4,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[4,3,4,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[1,5,5,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[2,4,5,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[3,3,5,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[4,2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[5,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[1,2,2,2,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[2,3,2,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[1,3,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[2,2,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[3,4,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[1,2,3,4,2]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[2,4,4,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[1,3,2,4,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[2,2,2,4,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[3,3,4,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[1,4,5,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[2,3,5,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[3,2,5,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[4,6,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[1,2,2,3,2,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[2,3,3,2,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[1,3,4,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[2,2,4,2,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[3,5,2,2]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[1,2,3,2,2,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[2,4,2,2,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[1,3,2,2,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[2,2,2,2,2,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[3,3,2,2,2]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[1,4,3,2,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[2,3,3,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[3,2,3,2,2]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[4,4,2,2]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[1,2,4,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[2,5,3,2]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[1,3,3,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[2,2,3,3,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[3,4,3,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[1,4,2,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[2,3,2,3,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[3,2,2,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[4,3,3,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[1,5,4,2]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[2,4,4,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[3,3,4,2]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[4,2,4,2]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[5,5,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[1,2,2,4,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[2,3,4,3]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[1,3,5,3]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[2,2,5,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[3,6,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[1,2,3,3,3]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[2,4,3,3]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[1,3,2,3,3]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[2,2,2,3,3]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[3,3,3,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[1,4,4,3]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[2,3,4,3]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[3,2,4,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[4,5,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[1,2,4,2,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[2,5,2,3]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[1,3,3,2,3]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[2,2,3,2,3]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[3,4,2,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[1,4,2,2,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[2,3,2,2,3]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[3,2,2,2,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[4,3,2,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[1,5,3,3]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[2,4,3,3]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[3,3,3,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[4,2,3,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[5,4,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[1,2,5,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[2,6,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[1,3,4,4]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[2,2,4,4]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[3,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[1,4,3,4]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[2,3,3,4]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[3,2,3,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[4,4,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[1,5,2,4]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[2,4,2,4]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[3,3,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[4,2,2,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[5,3,4]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[1,6,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[2,5,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[3,4,5]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[4,3,5]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[5,2,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[6,6]
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
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.
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
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
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