Identifier
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Images
=>
Cc0005;cc-rep-1Cc0002;cc-rep-3
[1]=>[1,0]=>[1]=>[1]
[1,1]=>[1,0,1,0]=>[1,2]=>[2]
[2]=>[1,1,0,0]=>[2,1]=>[1,1]
[1,1,1]=>[1,0,1,0,1,0]=>[1,2,3]=>[3]
[1,2]=>[1,0,1,1,0,0]=>[1,3,2]=>[2,1]
[2,1]=>[1,1,0,0,1,0]=>[2,1,3]=>[2,1]
[3]=>[1,1,1,0,0,0]=>[3,2,1]=>[1,1,1]
[1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4]
[1,1,2]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,1]
[1,2,1]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1]
[1,3]=>[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,1,1]
[2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[3,1]
[2,2]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,2]
[3,1]=>[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,1,1]
[4]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,1,1,1]
[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5]
[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,1]
[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1]
[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,1,1]
[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[4,1]
[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,2]
[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,1,1]
[1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,1,1,1]
[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[4,1]
[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2]
[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2]
[2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,2,1]
[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,1,1]
[3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,2,1]
[4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[2,1,1,1]
[5]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1]
[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6]
[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,1]
[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1]
[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,1,1]
[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[5,1]
[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[4,2]
[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[4,1,1]
[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,1,1,1]
[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[5,1]
[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[4,2]
[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[4,2]
[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[3,2,1]
[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,1,1]
[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[3,2,1]
[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[3,1,1,1]
[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[5,1]
[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[4,2]
[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[4,2]
[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[3,2,1]
[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[4,2]
[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[3,3]
[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[3,2,1]
[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,2,1,1]
[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[4,1,1]
[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1]
[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1]
[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,2,2]
[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[3,1,1,1]
[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[2,2,1,1]
[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[2,1,1,1,1]
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[7]
[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[6,1]
[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1]
[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[5,1,1]
[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[6,1]
[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[5,2]
[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[5,1,1]
[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[6,1]
[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[5,2]
[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[5,2]
[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[4,2,1]
[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,1,1]
[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,2,1]
[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[4,1,1,1]
[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[6,1]
[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[5,2]
[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[5,2]
[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[4,2,1]
[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[5,2]
[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[4,3]
[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[4,2,1]
[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[3,2,1,1]
[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[5,1,1]
[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,2,1]
[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,2,1]
[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[3,2,2]
[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[4,1,1,1]
[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[3,2,1,1]
[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[3,1,1,1,1]
[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[6,1]
[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[5,2]
[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[5,2]
[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[4,2,1]
[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[5,2]
[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[4,3]
[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[4,2,1]
[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[3,2,1,1]
[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[5,2]
[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[4,3]
[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[4,3]
[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[3,3,1]
[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[4,2,1]
[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[3,3,1]
[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[3,2,1,1]
[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,2,1,1,1]
[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[5,1,1]
[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[4,2,1]
[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,2,1]
[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,2]
[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,2,1]
[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,3,1]
[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,2]
[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[2,2,2,1]
[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,1,1,1]
[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[3,2,1,1]
[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[3,2,1,1]
[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[2,2,2,1]
[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[3,1,1,1,1]
[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[2,2,1,1,1]
[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[2,1,1,1,1,1]
[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8]
[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[7,1]
[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[7,1]
[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[7,1]
[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[6,2]
[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[6,1,1]
[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[7,1]
[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[6,2]
[1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[6,2]
[1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[5,2,1]
[1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[6,1,1]
[1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[5,2,1]
[1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[5,1,1,1]
[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[7,1]
[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[6,2]
[1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[6,2]
[1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[5,2,1]
[1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[6,2]
[1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[5,3]
[1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[4,2,1,1]
[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[6,1,1]
[1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[5,2,1]
[1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[5,1,1,1]
[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[4,1,1,1,1]
[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[7,1]
[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[6,2]
[1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[6,2]
[1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[5,2,1]
[1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[6,2]
[1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[5,3]
[1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[5,2,1]
[1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[4,2,1,1]
[1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[6,2]
[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[5,3]
[1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[4,3,1]
[1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[5,2,1]
[1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[4,3,1]
[1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[4,2,1,1]
[1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[3,2,1,1,1]
[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[6,1,1]
[1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[5,2,1]
[1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[5,2,1]
[1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[4,2,2]
[1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[4,2,2]
[1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[3,2,2,1]
[1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[5,1,1,1]
[1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[4,2,1,1]
[1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[3,2,2,1]
[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[4,1,1,1,1]
[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[3,2,1,1,1]
[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[3,1,1,1,1,1]
[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[7,1]
[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[6,2]
[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[6,2]
[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[5,2,1]
[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[6,2]
[2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[5,3]
[2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[4,2,1,1]
[2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[4,3,1]
[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[3,2,1,1,1]
[2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[6,2]
[2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[4,3,1]
[2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[5,3]
[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[4,4]
[2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[3,3,1,1]
[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[5,2,1]
[2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,4,3,7,6,8]=>[4,3,1]
[2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[3,3,1,1]
[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[3,2,1,1,1]
[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,2,1,1,1,1]
[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[6,1,1]
[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[5,2,1]
[3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[4,2,2]
[3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[4,2,2]
[3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,2,1]
[3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[4,3,1]
[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[3,2,2,1]
[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[2,2,2,1,1]
[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[5,1,1,1]
[4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[3,3,1,1]
[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2]
[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[4,1,1,1,1]
[5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[3,2,1,1,1]
[5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[3,2,1,1,1]
[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[2,2,2,1,1]
[6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[3,1,1,1,1,1]
[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[2,2,1,1,1,1]
[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,1]
[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[9]
[1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[8,1]
[1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[8,1]
[1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[7,1,1]
[1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[8,1]
[1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>[7,2]
[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[6,1,1,1]
[1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[8,1]
[1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[7,2]
[1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1]
[1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[8,1]
[1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[6,3]
[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[4,1,1,1,1,1]
[1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[8,1]
[1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[6,3]
[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[8,1]
[1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[7,2]
[1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>[6,2,1]
[1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>[7,2]
[1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[5,4]
[1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[7,1,1]
[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>[3,2,1,1,1,1]
[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[3,1,1,1,1,1,1]
[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[8,1]
[2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[7,2]
[2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[7,2]
[2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[7,2]
[2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[5,4]
[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[3,2,1,1,1,1]
[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1]
[3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[7,1,1]
[3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>[4,4,1]
[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[2,2,2,1,1,1]
[4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[6,1,1,1]
[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[2,2,2,2,1]
[5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[5,1,1,1,1]
[5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[2,2,2,2,1]
[6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[4,1,1,1,1,1]
[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[2,2,2,1,1,1]
[7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[3,1,1,1,1,1,1]
[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[2,2,1,1,1,1,1]
[8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,1]
[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[9,1]
[1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[9,1]
[1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[8,1,1]
[1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[9,1]
[1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[7,1,1,1]
[1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[9,1]
[1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1]
[1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[9,1]
[1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1]
[1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[9,1]
[1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>[7,3]
[1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[4,1,1,1,1,1,1]
[1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[9,1]
[1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1]
[1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[9,1]
[1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[6,4]
[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[3,1,1,1,1,1,1,1]
[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[9,1]
[2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[8,2]
[2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[5,5]
[2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,10,9,8,7]=>[4,4,1,1]
[2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[3,3,2,2]
[2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[3,3,1,1,1,1]
[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[2,2,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[8,1,1]
[3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[5,4,1]
[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[2,2,2,1,1,1,1]
[4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[7,1,1,1]
[4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[4,4,1,1]
[4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[3,3,2,2]
[4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[3,3,2,2]
[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[2,2,2,2,1,1]
[5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[6,1,1,1,1]
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[2,2,2,2,2]
[6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[5,1,1,1,1,1]
[6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[2,2,2,2,1,1]
[7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[4,1,1,1,1,1,1]
[7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[2,2,2,1,1,1,1]
[8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[3,1,1,1,1,1,1,1]
[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[2,2,1,1,1,1,1,1]
[9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[2,1,1,1,1,1,1,1,1]
[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]
[10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[6,6]
[1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,1]
[1,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[6,5]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
searching the database
Sorry, this map was not found in the database.