Identifier
Mp00231:
Integer compositions
—bounce path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-1Cc0005;cc-rep-3
[1]=>[1,0]=>[2,1]=>[1,1,0,0]
[1,1]=>[1,0,1,0]=>[3,1,2]=>[1,1,1,0,0,0]
[2]=>[1,1,0,0]=>[2,3,1]=>[1,1,0,1,0,0]
[1,1,1]=>[1,0,1,0,1,0]=>[4,1,2,3]=>[1,1,1,1,0,0,0,0]
[1,2]=>[1,0,1,1,0,0]=>[3,1,4,2]=>[1,1,1,0,0,1,0,0]
[2,1]=>[1,1,0,0,1,0]=>[2,4,1,3]=>[1,1,0,1,1,0,0,0]
[3]=>[1,1,1,0,0,0]=>[2,3,4,1]=>[1,1,0,1,0,1,0,0]
[1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,2]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]
[1,2,1]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[1,1,1,0,0,1,1,0,0,0]
[1,3]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[1,1,0,1,1,1,0,0,0,0]
[2,2]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]
[3,1]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[1,1,0,1,0,1,1,0,0,0]
[4]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[10,1,2,3,4,5,6,7,8,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[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]=>[9,1,2,3,4,5,6,7,10,8]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[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]=>[8,1,2,3,4,5,6,9,10,7]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]
[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]=>[7,1,2,3,4,5,9,6,10,8]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]
[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]=>[5,1,2,3,10,4,6,7,8,9]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[4,1,2,10,3,5,6,7,8,9]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[3,1,9,2,4,5,6,7,10,8]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[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]=>[3,1,5,2,10,4,6,7,8,9]=>[1,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[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]=>[3,1,4,10,2,5,6,7,8,9]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,7,9,2,10,8]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,10,1,3,4,5,6,7,8,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[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]=>[2,9,1,3,4,5,6,7,10,8]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]
[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]=>[2,8,1,3,4,5,6,10,7,9]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]
[2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,10,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
[2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,8,10,3,9]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,3,10,1,4,5,6,7,8,9]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,10,1,7,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[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]=>[10,1,2,3,4,5,6,7,8,11,9]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
[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]=>[7,1,2,3,4,5,11,6,8,9,10]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
[1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,11,1,3,4,5,6,7,8,9,10]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[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]=>[2,10,1,3,4,5,6,7,8,11,9]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]
[2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,3,11,1,4,5,6,7,8,9,10]=>[1,1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
[3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,3,4,11,1,5,6,7,8,9,10]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,3,4,5,11,1,6,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[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]=>[2,3,4,5,6,11,1,7,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[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]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]
[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]=>[3,1,5,2,7,4,9,6,11,8,12,10]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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