Identifier
Mp00201:
Dyck paths
—Ringel⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00066: Permutations —inverse⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0009;cc-rep-3
[1,0]=>[2,1]=>[2,1]=>{{1,2}}
[1,0,1,0]=>[3,1,2]=>[2,3,1]=>{{1,2,3}}
[1,1,0,0]=>[2,3,1]=>[3,1,2]=>{{1,3},{2}}
[1,0,1,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>{{1,2,3,4}}
[1,0,1,1,0,0]=>[3,1,4,2]=>[2,4,1,3]=>{{1,2,4},{3}}
[1,1,0,0,1,0]=>[2,4,1,3]=>[3,1,4,2]=>{{1,3,4},{2}}
[1,1,0,1,0,0]=>[4,3,1,2]=>[3,4,2,1]=>{{1,3},{2,4}}
[1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3]=>{{1,4},{2},{3}}
[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[2,3,5,1,4]=>{{1,2,3,5},{4}}
[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[2,4,1,5,3]=>{{1,2,4,5},{3}}
[1,0,1,1,0,1,0,0]=>[5,1,4,2,3]=>[2,4,5,3,1]=>{{1,2,4},{3,5}}
[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}}
[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[3,1,4,5,2]=>{{1,3,4,5},{2}}
[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}}
[1,1,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,4,2,5,1]=>{{1,3},{2,4,5}}
[1,1,0,1,0,1,0,0]=>[5,4,1,2,3]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}
[1,1,0,1,1,0,0,0]=>[4,3,1,5,2]=>[3,5,2,1,4]=>{{1,3},{2,5},{4}}
[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}}
[1,1,1,0,0,1,0,0]=>[2,5,4,1,3]=>[4,1,5,3,2]=>{{1,4},{2},{3,5}}
[1,1,1,0,1,0,0,0]=>[5,3,4,1,2]=>[4,5,2,3,1]=>{{1,4},{2,5},{3}}
[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}}
[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}}
[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}}
[1,0,1,0,1,1,0,1,0,0]=>[6,1,2,5,3,4]=>[2,3,5,6,4,1]=>{{1,2,3,5},{4,6}}
[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}}
[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}}
[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}}
[1,0,1,1,0,1,0,0,1,0]=>[6,1,4,2,3,5]=>[2,4,5,3,6,1]=>{{1,2,4},{3,5,6}}
[1,0,1,1,0,1,0,1,0,0]=>[6,1,5,2,3,4]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}
[1,0,1,1,0,1,1,0,0,0]=>[5,1,4,2,6,3]=>[2,4,6,3,1,5]=>{{1,2,4},{3,6},{5}}
[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}}
[1,0,1,1,1,0,0,1,0,0]=>[3,1,6,5,2,4]=>[2,5,1,6,4,3]=>{{1,2,5},{3},{4,6}}
[1,0,1,1,1,0,1,0,0,0]=>[6,1,4,5,2,3]=>[2,5,6,3,4,1]=>{{1,2,5},{3,6},{4}}
[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}}
[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}}
[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}}
[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}}
[1,1,0,0,1,1,0,1,0,0]=>[2,6,1,5,3,4]=>[3,1,5,6,4,2]=>{{1,3,5},{2},{4,6}}
[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}}
[1,1,0,1,0,0,1,0,1,0]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>{{1,3},{2,4,5,6}}
[1,1,0,1,0,0,1,1,0,0]=>[5,3,1,2,6,4]=>[3,4,2,6,1,5]=>{{1,3},{2,4,6},{5}}
[1,1,0,1,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[1,1,0,1,0,1,0,1,0,0]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}
[1,1,0,1,0,1,1,0,0,0]=>[5,4,1,2,6,3]=>[3,4,6,2,1,5]=>{{1,3,6},{2,4},{5}}
[1,1,0,1,1,0,0,0,1,0]=>[4,3,1,6,2,5]=>[3,5,2,1,6,4]=>{{1,3},{2,5,6},{4}}
[1,1,0,1,1,0,0,1,0,0]=>[6,3,1,5,2,4]=>[3,5,2,6,4,1]=>{{1,3},{2,5},{4,6}}
[1,1,0,1,1,0,1,0,0,0]=>[6,4,1,5,2,3]=>[3,5,6,2,4,1]=>{{1,3,6},{2,5},{4}}
[1,1,0,1,1,1,0,0,0,0]=>[4,3,1,5,6,2]=>[3,6,2,1,4,5]=>{{1,3},{2,6},{4},{5}}
[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}}
[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}}
[1,1,1,0,0,1,0,0,1,0]=>[2,6,4,1,3,5]=>[4,1,5,3,6,2]=>{{1,4},{2},{3,5,6}}
[1,1,1,0,0,1,0,1,0,0]=>[2,6,5,1,3,4]=>[4,1,5,6,3,2]=>{{1,4,6},{2},{3,5}}
[1,1,1,0,0,1,1,0,0,0]=>[2,5,4,1,6,3]=>[4,1,6,3,2,5]=>{{1,4},{2},{3,6},{5}}
[1,1,1,0,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>{{1,4},{2,5,6},{3}}
[1,1,1,0,1,0,0,1,0,0]=>[6,3,5,1,2,4]=>[4,5,2,6,3,1]=>{{1,4,6},{2,5},{3}}
[1,1,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}
[1,1,1,0,1,1,0,0,0,0]=>[5,3,4,1,6,2]=>[4,6,2,3,1,5]=>{{1,4},{2,6},{3},{5}}
[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}}
[1,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,1,4]=>[5,1,2,6,4,3]=>{{1,5},{2},{3},{4,6}}
[1,1,1,1,0,0,1,0,0,0]=>[2,6,4,5,1,3]=>[5,1,6,3,4,2]=>{{1,5},{2},{3,6},{4}}
[1,1,1,1,0,1,0,0,0,0]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>{{1,5},{2,6},{3},{4}}
[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}}
[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,7},{6}}
[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,6,7},{5}}
[1,0,1,0,1,0,1,1,0,1,0,0]=>[7,1,2,3,6,4,5]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,6},{5,7}}
[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,7},{5},{6}}
[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[2,3,5,1,6,7,4]=>{{1,2,3,5,6,7},{4}}
[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[2,3,5,1,7,4,6]=>{{1,2,3,5,7},{4},{6}}
[1,0,1,0,1,1,0,1,0,0,1,0]=>[7,1,2,5,3,4,6]=>[2,3,5,6,4,7,1]=>{{1,2,3,5},{4,6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0]=>[7,1,2,6,3,4,5]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[1,0,1,0,1,1,0,1,1,0,0,0]=>[6,1,2,5,3,7,4]=>[2,3,5,7,4,1,6]=>{{1,2,3,5},{4,7},{6}}
[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[2,3,6,1,4,7,5]=>{{1,2,3,6,7},{4},{5}}
[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,1,2,7,6,3,5]=>[2,3,6,1,7,5,4]=>{{1,2,3,6},{4},{5,7}}
[1,0,1,0,1,1,1,0,1,0,0,0]=>[7,1,2,5,6,3,4]=>[2,3,6,7,4,5,1]=>{{1,2,3,6},{4,7},{5}}
[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[2,3,7,1,4,5,6]=>{{1,2,3,7},{4},{5},{6}}
[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[2,4,1,5,6,7,3]=>{{1,2,4,5,6,7},{3}}
[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[2,4,1,5,7,3,6]=>{{1,2,4,5,7},{3},{6}}
[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[2,4,1,6,3,7,5]=>{{1,2,4,6,7},{3},{5}}
[1,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,7,2,6,4,5]=>[2,4,1,6,7,5,3]=>{{1,2,4,6},{3},{5,7}}
[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[2,4,1,7,3,5,6]=>{{1,2,4,7},{3},{5},{6}}
[1,0,1,1,0,1,0,0,1,0,1,0]=>[7,1,4,2,3,5,6]=>[2,4,5,3,6,7,1]=>{{1,2,4},{3,5,6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0]=>[6,1,4,2,3,7,5]=>[2,4,5,3,7,1,6]=>{{1,2,4},{3,5,7},{6}}
[1,0,1,1,0,1,0,1,0,0,1,0]=>[7,1,5,2,3,4,6]=>[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}
[1,0,1,1,0,1,0,1,0,1,0,0]=>[6,1,7,2,3,4,5]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}
[1,0,1,1,0,1,0,1,1,0,0,0]=>[6,1,5,2,3,7,4]=>[2,4,5,7,3,1,6]=>{{1,2,4,7},{3,5},{6}}
[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,1,4,2,7,3,6]=>[2,4,6,3,1,7,5]=>{{1,2,4},{3,6,7},{5}}
[1,0,1,1,0,1,1,0,0,1,0,0]=>[7,1,4,2,6,3,5]=>[2,4,6,3,7,5,1]=>{{1,2,4},{3,6},{5,7}}
[1,0,1,1,0,1,1,0,1,0,0,0]=>[7,1,5,2,6,3,4]=>[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,6},{5}}
[1,0,1,1,0,1,1,1,0,0,0,0]=>[5,1,4,2,6,7,3]=>[2,4,7,3,1,5,6]=>{{1,2,4},{3,7},{5},{6}}
[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[2,5,1,3,6,7,4]=>{{1,2,5,6,7},{3},{4}}
[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[2,5,1,3,7,4,6]=>{{1,2,5,7},{3},{4},{6}}
[1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,7,5,2,4,6]=>[2,5,1,6,4,7,3]=>{{1,2,5},{3},{4,6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,7,6,2,4,5]=>[2,5,1,6,7,4,3]=>{{1,2,5,7},{3},{4,6}}
[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,6,5,2,7,4]=>[2,5,1,7,4,3,6]=>{{1,2,5},{3},{4,7},{6}}
[1,0,1,1,1,0,1,0,0,0,1,0]=>[7,1,4,5,2,3,6]=>[2,5,6,3,4,7,1]=>{{1,2,5},{3,6,7},{4}}
[1,0,1,1,1,0,1,0,0,1,0,0]=>[7,1,4,6,2,3,5]=>[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,6},{4}}
[1,0,1,1,1,0,1,0,1,0,0,0]=>[7,1,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>{{1,2,5},{3,6},{4,7}}
[1,0,1,1,1,0,1,1,0,0,0,0]=>[6,1,4,5,2,7,3]=>[2,5,7,3,4,1,6]=>{{1,2,5},{3,7},{4},{6}}
[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[2,6,1,3,4,7,5]=>{{1,2,6,7},{3},{4},{5}}
[1,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,6,2,5]=>[2,6,1,3,7,5,4]=>{{1,2,6},{3},{4},{5,7}}
[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,7,5,6,2,4]=>[2,6,1,7,4,5,3]=>{{1,2,6},{3},{4,7},{5}}
[1,0,1,1,1,1,0,1,0,0,0,0]=>[7,1,4,5,6,2,3]=>[2,6,7,3,4,5,1]=>{{1,2,6},{3,7},{4},{5}}
[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>{{1,2,7},{3},{4},{5},{6}}
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>{{1,3,4,5,6,7},{2}}
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[3,1,4,5,7,2,6]=>{{1,3,4,5,7},{2},{6}}
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[3,1,4,6,2,7,5]=>{{1,3,4,6,7},{2},{5}}
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,7,1,3,6,4,5]=>[3,1,4,6,7,5,2]=>{{1,3,4,6},{2},{5,7}}
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[3,1,4,7,2,5,6]=>{{1,3,4,7},{2},{5},{6}}
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[3,1,5,2,6,7,4]=>{{1,3,5,6,7},{2},{4}}
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[3,1,5,2,7,4,6]=>{{1,3,5,7},{2},{4},{6}}
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,7,1,5,3,4,6]=>[3,1,5,6,4,7,2]=>{{1,3,5},{2},{4,6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,7,1,6,3,4,5]=>[3,1,5,6,7,4,2]=>{{1,3,5,7},{2},{4,6}}
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,6,1,5,3,7,4]=>[3,1,5,7,4,2,6]=>{{1,3,5},{2},{4,7},{6}}
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[3,1,6,2,4,7,5]=>{{1,3,6,7},{2},{4},{5}}
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,6,3,5]=>[3,1,6,2,7,5,4]=>{{1,3,6},{2},{4},{5,7}}
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,7,1,5,6,3,4]=>[3,1,6,7,4,5,2]=>{{1,3,6},{2},{4,7},{5}}
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[3,1,7,2,4,5,6]=>{{1,3,7},{2},{4},{5},{6}}
[1,1,0,1,0,0,1,0,1,0,1,0]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>{{1,3},{2,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0]=>[6,3,1,2,4,7,5]=>[3,4,2,5,7,1,6]=>{{1,3},{2,4,5,7},{6}}
[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,1,2,7,4,6]=>[3,4,2,6,1,7,5]=>{{1,3},{2,4,6,7},{5}}
[1,1,0,1,0,0,1,1,0,1,0,0]=>[7,3,1,2,6,4,5]=>[3,4,2,6,7,5,1]=>{{1,3},{2,4,6},{5,7}}
[1,1,0,1,0,0,1,1,1,0,0,0]=>[5,3,1,2,6,7,4]=>[3,4,2,7,1,5,6]=>{{1,3},{2,4,7},{5},{6}}
[1,1,0,1,0,1,0,0,1,0,1,0]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[1,1,0,1,0,1,0,0,1,1,0,0]=>[6,4,1,2,3,7,5]=>[3,4,5,2,7,1,6]=>{{1,3,5,7},{2,4},{6}}
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,7,1,2,3,4,6]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,1,2,3,7,4]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,7},{6}}
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,4,1,2,7,3,6]=>[3,4,6,2,1,7,5]=>{{1,3,6,7},{2,4},{5}}
[1,1,0,1,0,1,1,0,0,1,0,0]=>[7,4,1,2,6,3,5]=>[3,4,6,2,7,5,1]=>{{1,3,6},{2,4},{5,7}}
[1,1,0,1,0,1,1,0,1,0,0,0]=>[5,7,1,2,6,3,4]=>[3,4,6,7,1,5,2]=>{{1,3,6},{2,4,7},{5}}
[1,1,0,1,0,1,1,1,0,0,0,0]=>[5,4,1,2,6,7,3]=>[3,4,7,2,1,5,6]=>{{1,3,7},{2,4},{5},{6}}
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,3,1,7,2,5,6]=>[3,5,2,1,6,7,4]=>{{1,3},{2,5,6,7},{4}}
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,3,1,6,2,7,5]=>[3,5,2,1,7,4,6]=>{{1,3},{2,5,7},{4},{6}}
[1,1,0,1,1,0,0,1,0,0,1,0]=>[7,3,1,5,2,4,6]=>[3,5,2,6,4,7,1]=>{{1,3},{2,5},{4,6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0]=>[7,3,1,6,2,4,5]=>[3,5,2,6,7,4,1]=>{{1,3},{2,5,7},{4,6}}
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6,3,1,5,2,7,4]=>[3,5,2,7,4,1,6]=>{{1,3},{2,5},{4,7},{6}}
[1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,1,5,2,3,6]=>[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,5},{4}}
[1,1,0,1,1,0,1,0,0,1,0,0]=>[7,4,1,6,2,3,5]=>[3,5,6,2,7,4,1]=>{{1,3,6},{2,5,7},{4}}
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6,7,1,5,2,3,4]=>[3,5,6,7,4,1,2]=>{{1,3,6},{2,5},{4,7}}
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6,4,1,5,2,7,3]=>[3,5,7,2,4,1,6]=>{{1,3,7},{2,5},{4},{6}}
[1,1,0,1,1,1,0,0,0,0,1,0]=>[4,3,1,5,7,2,6]=>[3,6,2,1,4,7,5]=>{{1,3},{2,6,7},{4},{5}}
[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,3,1,7,6,2,5]=>[3,6,2,1,7,5,4]=>{{1,3},{2,6},{4},{5,7}}
[1,1,0,1,1,1,0,0,1,0,0,0]=>[7,3,1,5,6,2,4]=>[3,6,2,7,4,5,1]=>{{1,3},{2,6},{4,7},{5}}
[1,1,0,1,1,1,0,1,0,0,0,0]=>[7,4,1,5,6,2,3]=>[3,6,7,2,4,5,1]=>{{1,3,7},{2,6},{4},{5}}
[1,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,1,5,6,7,2]=>[3,7,2,1,4,5,6]=>{{1,3},{2,7},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[4,1,2,5,6,7,3]=>{{1,4,5,6,7},{2},{3}}
[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[4,1,2,5,7,3,6]=>{{1,4,5,7},{2},{3},{6}}
[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[4,1,2,6,3,7,5]=>{{1,4,6,7},{2},{3},{5}}
[1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,7,1,6,4,5]=>[4,1,2,6,7,5,3]=>{{1,4,6},{2},{3},{5,7}}
[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[4,1,2,7,3,5,6]=>{{1,4,7},{2},{3},{5},{6}}
[1,1,1,0,0,1,0,0,1,0,1,0]=>[2,7,4,1,3,5,6]=>[4,1,5,3,6,7,2]=>{{1,4},{2},{3,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,4,1,3,7,5]=>[4,1,5,3,7,2,6]=>{{1,4},{2},{3,5,7},{6}}
[1,1,1,0,0,1,0,1,0,0,1,0]=>[2,7,5,1,3,4,6]=>[4,1,5,6,3,7,2]=>{{1,4,6,7},{2},{3,5}}
[1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6,7,1,3,4,5]=>[4,1,5,6,7,2,3]=>{{1,4,6},{2},{3,5,7}}
[1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6,5,1,3,7,4]=>[4,1,5,7,3,2,6]=>{{1,4,7},{2},{3,5},{6}}
[1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,4,1,7,3,6]=>[4,1,6,3,2,7,5]=>{{1,4},{2},{3,6,7},{5}}
[1,1,1,0,0,1,1,0,0,1,0,0]=>[2,7,4,1,6,3,5]=>[4,1,6,3,7,5,2]=>{{1,4},{2},{3,6},{5,7}}
[1,1,1,0,0,1,1,0,1,0,0,0]=>[2,7,5,1,6,3,4]=>[4,1,6,7,3,5,2]=>{{1,4,7},{2},{3,6},{5}}
[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,5,4,1,6,7,3]=>[4,1,7,3,2,5,6]=>{{1,4},{2},{3,7},{5},{6}}
[1,1,1,0,1,0,0,0,1,0,1,0]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>{{1,4},{2,5,6,7},{3}}
[1,1,1,0,1,0,0,0,1,1,0,0]=>[6,3,4,1,2,7,5]=>[4,5,2,3,7,1,6]=>{{1,4},{2,5,7},{3},{6}}
[1,1,1,0,1,0,0,1,0,0,1,0]=>[7,3,5,1,2,4,6]=>[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,5},{3}}
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6,3,7,1,2,4,5]=>[4,5,2,6,7,1,3]=>{{1,4,6},{2,5,7},{3}}
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6,3,5,1,2,7,4]=>[4,5,2,7,3,1,6]=>{{1,4,7},{2,5},{3},{6}}
[1,1,1,0,1,0,1,0,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>{{1,4},{2,5},{3,6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>{{1,4},{2,5,7},{3,6}}
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>{{1,4,7},{2,5},{3,6}}
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6,5,4,1,2,7,3]=>[4,5,7,3,2,1,6]=>{{1,4},{2,5},{3,7},{6}}
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,3,4,1,7,2,6]=>[4,6,2,3,1,7,5]=>{{1,4},{2,6,7},{3},{5}}
[1,1,1,0,1,1,0,0,0,1,0,0]=>[7,3,4,1,6,2,5]=>[4,6,2,3,7,5,1]=>{{1,4},{2,6},{3},{5,7}}
[1,1,1,0,1,1,0,0,1,0,0,0]=>[7,3,5,1,6,2,4]=>[4,6,2,7,3,5,1]=>{{1,4,7},{2,6},{3},{5}}
[1,1,1,0,1,1,0,1,0,0,0,0]=>[7,5,4,1,6,2,3]=>[4,6,7,3,2,5,1]=>{{1,4},{2,6},{3,7},{5}}
[1,1,1,0,1,1,1,0,0,0,0,0]=>[5,3,4,1,6,7,2]=>[4,7,2,3,1,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[5,1,2,3,6,7,4]=>{{1,5,6,7},{2},{3},{4}}
[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[5,1,2,3,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}
[1,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,7,5,1,4,6]=>[5,1,2,6,4,7,3]=>{{1,5},{2},{3},{4,6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,7,6,1,4,5]=>[5,1,2,6,7,4,3]=>{{1,5,7},{2},{3},{4,6}}
[1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,1,7,4]=>[5,1,2,7,4,3,6]=>{{1,5},{2},{3},{4,7},{6}}
[1,1,1,1,0,0,1,0,0,0,1,0]=>[2,7,4,5,1,3,6]=>[5,1,6,3,4,7,2]=>{{1,5},{2},{3,6,7},{4}}
[1,1,1,1,0,0,1,0,0,1,0,0]=>[2,7,4,6,1,3,5]=>[5,1,6,3,7,4,2]=>{{1,5,7},{2},{3,6},{4}}
[1,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,6,5,1,3,4]=>[5,1,6,7,4,3,2]=>{{1,5},{2},{3,6},{4,7}}
[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6,4,5,1,7,3]=>[5,1,7,3,4,2,6]=>{{1,5},{2},{3,7},{4},{6}}
[1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>{{1,5},{2,6,7},{3},{4}}
[1,1,1,1,0,1,0,0,0,1,0,0]=>[7,3,4,6,1,2,5]=>[5,6,2,3,7,4,1]=>{{1,5,7},{2,6},{3},{4}}
[1,1,1,1,0,1,0,0,1,0,0,0]=>[7,3,6,5,1,2,4]=>[5,6,2,7,4,3,1]=>{{1,5},{2,6},{3},{4,7}}
[1,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>{{1,5},{2,6},{3,7},{4}}
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,4,5,1,7,2]=>[5,7,2,3,4,1,6]=>{{1,5},{2,7},{3},{4},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[6,1,2,3,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,7,6,1,5]=>[6,1,2,3,7,5,4]=>{{1,6},{2},{3},{4},{5,7}}
[1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,5,6,1,4]=>[6,1,2,7,4,5,3]=>{{1,6},{2},{3},{4,7},{5}}
[1,1,1,1,1,0,0,1,0,0,0,0]=>[2,7,4,5,6,1,3]=>[6,1,7,3,4,5,2]=>{{1,6},{2},{3,7},{4},{5}}
[1,1,1,1,1,0,1,0,0,0,0,0]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>{{1,6},{2,7},{3},{4},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,8},{7}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,7,8},{6}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,8},{6},{7}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,8},{5},{6},{7}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,5,6,7,8},{4}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,5,7,8},{4},{6}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,1,2,8,3,4,5,6]=>[2,3,5,6,7,8,1,4]=>{{1,2,3,5,7},{4,6,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[4,1,2,8,7,3,5,6]=>[2,3,6,1,7,8,5,4]=>{{1,2,3,6,8},{4},{5,7}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,1,2,5,6,3,4,7]=>[2,3,6,7,4,5,8,1]=>{{1,2,3,6},{4,7,8},{5}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[2,4,1,5,6,7,8,3]=>{{1,2,4,5,6,7,8},{3}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[2,4,1,6,3,7,8,5]=>{{1,2,4,6,7,8},{3},{5}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>[2,4,1,6,3,8,5,7]=>{{1,2,4,6,8},{3},{5},{7}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,7,2,6,4,8,5]=>[2,4,1,6,8,5,3,7]=>{{1,2,4,6},{3},{5,8},{7}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,5,2,8,7,4,6]=>[2,4,1,7,3,8,6,5]=>{{1,2,4,7},{3},{5},{6,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,1,4,2,3,8,5,7]=>[2,4,5,3,7,1,8,6]=>{{1,2,4},{3,5,7,8},{6}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[8,1,4,2,3,7,5,6]=>[2,4,5,3,7,8,6,1]=>{{1,2,4},{3,5,7},{6,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,1,8,2,3,4,5,7]=>[2,4,5,6,7,1,8,3]=>{{1,2,4,6},{3,5,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,1,5,2,3,8,4,7]=>[2,4,5,7,3,1,8,6]=>{{1,2,4,7,8},{3,5},{6}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,1,4,2,7,3,8,6]=>[2,4,6,3,1,8,5,7]=>{{1,2,4},{3,6,8},{5},{7}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,1,4,2,6,3,5,7]=>[2,4,6,3,7,5,8,1]=>{{1,2,4},{3,6},{5,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[7,1,4,2,6,3,8,5]=>[2,4,6,3,8,5,1,7]=>{{1,2,4},{3,6},{5,8},{7}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[8,1,5,2,7,3,4,6]=>[2,4,6,7,3,8,5,1]=>{{1,2,4,7},{3,6,8},{5}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[7,1,5,2,6,3,8,4]=>[2,4,6,8,3,5,1,7]=>{{1,2,4,8},{3,6},{5},{7}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,8,6,2,4,5,7]=>[2,5,1,6,7,4,8,3]=>{{1,2,5,7,8},{3},{4,6}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,7,8,2,4,5,6]=>[2,5,1,6,7,8,3,4]=>{{1,2,5,7},{3},{4,6,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,1,4,5,2,3,6,7]=>[2,5,6,3,4,7,8,1]=>{{1,2,5},{3,6,7,8},{4}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[7,1,8,6,2,3,4,5]=>[2,5,6,7,8,4,1,3]=>{{1,2,5,8},{3,6},{4,7}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,4,5,8,7,2,6]=>[2,7,1,3,4,8,6,5]=>{{1,2,7},{3},{4},{5},{6,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[8,1,4,5,6,7,2,3]=>[2,7,8,3,4,5,6,1]=>{{1,2,7},{3,8},{4},{5},{6}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[2,8,1,3,4,5,6,7]=>{{1,2,8},{3},{4},{5},{6},{7}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>[3,1,4,5,6,7,8,2]=>{{1,3,4,5,6,7,8},{2}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,8,1,3,4,7,5,6]=>[3,1,4,5,7,8,6,2]=>{{1,3,4,5,7},{2},{6,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>[3,1,5,2,7,4,8,6]=>{{1,3,5,7,8},{2},{4},{6}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>[3,1,5,2,8,4,6,7]=>{{1,3,5,8},{2},{4},{6},{7}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1,8,6,3,5,7]=>[3,1,6,2,7,5,8,4]=>{{1,3,6},{2},{4},{5,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,8,1,5,7,3,4,6]=>[3,1,6,7,4,8,5,2]=>{{1,3,6,8},{2},{4,7},{5}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[3,1,8,2,4,5,6,7]=>{{1,3,8},{2},{4},{5},{6},{7}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>{{1,3},{2,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,3,1,2,4,5,8,6]=>[3,4,2,5,6,8,1,7]=>{{1,3},{2,4,5,6,8},{7}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[8,3,1,2,4,7,5,6]=>[3,4,2,5,7,8,6,1]=>{{1,3},{2,4,5,7},{6,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,3,1,2,6,4,5,7]=>[3,4,2,6,7,5,8,1]=>{{1,3},{2,4,6},{5,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>{{1,3,5,6,7,8},{2,4}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[5,6,1,2,3,8,4,7]=>[3,4,5,7,1,2,8,6]=>{{1,3,5},{2,4,7,8},{6}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,1,2,3,7,8,4]=>[3,4,5,8,1,2,6,7]=>{{1,3,5},{2,4,8},{6},{7}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,8,3,6,7]=>[3,4,6,2,1,7,8,5]=>{{1,3,6,7,8},{2,4},{5}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,4,1,2,7,3,5,6]=>[3,4,6,2,7,8,5,1]=>{{1,3,6,8},{2,4},{5,7}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,8,1,2,7,3,4,6]=>[3,4,6,7,1,8,5,2]=>{{1,3,6,8},{2,4,7},{5}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8,3,1,5,2,7,4,6]=>[3,5,2,7,4,8,6,1]=>{{1,3},{2,5},{4,7},{6,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,4,1,5,2,3,8,6]=>[3,5,6,2,4,8,1,7]=>{{1,3,6,8},{2,5},{4},{7}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,4,1,6,2,3,5,7]=>[3,5,6,2,7,4,8,1]=>{{1,3,6},{2,5,7,8},{4}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,4,1,8,2,3,5,6]=>[3,5,6,2,7,8,1,4]=>{{1,3,6,8},{2,5,7},{4}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8,7,1,6,2,3,4,5]=>[3,5,6,7,8,4,2,1]=>{{1,3,6},{2,5,8},{4,7}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,4,1,5,2,8,3,7]=>[3,5,7,2,4,1,8,6]=>{{1,3,7,8},{2,5},{4},{6}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,3,1,5,6,2,4,7]=>[3,6,2,7,4,5,8,1]=>{{1,3},{2,6},{4,7,8},{5}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8,3,1,5,7,2,4,6]=>[3,6,2,7,4,8,5,1]=>{{1,3},{2,6,8},{4,7},{5}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8,3,1,7,6,2,4,5]=>[3,6,2,7,8,5,4,1]=>{{1,3},{2,6},{4,7},{5,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7,3,1,5,6,2,8,4]=>[3,6,2,8,4,5,1,7]=>{{1,3},{2,6},{4,8},{5},{7}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,3,1,5,6,8,2,7]=>[3,7,2,1,4,5,8,6]=>{{1,3},{2,7,8},{4},{5},{6}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>[4,1,2,5,6,7,8,3]=>{{1,4,5,6,7,8},{2},{3}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>[4,1,2,6,3,8,5,7]=>{{1,4,6,8},{2},{3},{5},{7}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,3,5,1,8,7,4,6]=>[4,1,2,7,3,8,6,5]=>{{1,4,7},{2},{3},{5},{6,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,3,8,1,6,7,4,5]=>[4,1,2,7,8,5,6,3]=>{{1,4,7},{2},{3},{5,8},{6}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,6,4,1,3,8,5,7]=>[4,1,5,3,7,2,8,6]=>{{1,4},{2},{3,5,7,8},{6}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,4,1,3,7,8,5]=>[4,1,5,3,8,2,6,7]=>{{1,4},{2},{3,5,8},{6},{7}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,7,5,1,3,4,8,6]=>[4,1,5,6,3,8,2,7]=>{{1,4,6,8},{2},{3,5},{7}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[4,1,5,6,8,2,3,7]=>{{1,4,6},{2},{3,5,8},{7}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,6,8,1,3,7,4,5]=>[4,1,5,7,8,2,6,3]=>{{1,4,7},{2},{3,5,8},{6}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,6,5,1,3,7,8,4]=>[4,1,5,8,3,2,6,7]=>{{1,4,8},{2},{3,5},{6},{7}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,8,4,1,6,3,5,7]=>[4,1,6,3,7,5,8,2]=>{{1,4},{2},{3,6},{5,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,8,4,1,6,7,3,5]=>[4,1,7,3,8,5,6,2]=>{{1,4},{2},{3,7},{5,8},{6}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3,4,1,2,7,8,5]=>[4,5,2,3,8,1,6,7]=>{{1,4},{2,5,8},{3},{6},{7}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,3,5,1,2,4,6,7]=>[4,5,2,6,3,7,8,1]=>{{1,4,6,7,8},{2,5},{3}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,3,5,1,2,4,8,6]=>[4,5,2,6,3,8,1,7]=>{{1,4,6,8},{2,5},{3},{7}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8,3,5,1,2,7,4,6]=>[4,5,2,7,3,8,6,1]=>{{1,4,7},{2,5},{3},{6,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,3,8,1,2,7,4,5]=>[4,5,2,7,8,1,6,3]=>{{1,4,7},{2,5,8},{3},{6}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,5,4,1,2,3,8,6]=>[4,5,6,3,2,8,1,7]=>{{1,4},{2,5},{3,6,8},{7}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,8,5,1,2,3,4,7]=>[4,5,6,7,3,1,8,2]=>{{1,4,7,8},{2,5},{3,6}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>{{1,4,7},{2,5},{3,6,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>{{1,4,7},{2,5,8},{3,6}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,4,1,2,7,3,6]=>[4,5,7,3,2,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[6,8,5,1,2,7,3,4]=>[4,5,7,8,3,1,6,2]=>{{1,4,8},{2,5},{3,7},{6}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,3,5,1,6,2,8,4]=>[4,6,2,8,3,5,1,7]=>{{1,4,8},{2,6},{3},{5},{7}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7,8,4,1,6,2,3,5]=>[4,6,7,3,8,5,1,2]=>{{1,4},{2,6},{3,7},{5,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7,8,5,1,6,2,3,4]=>[4,6,7,8,3,5,1,2]=>{{1,4,8},{2,6},{3,7},{5}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8,3,4,1,6,7,2,5]=>[4,7,2,3,8,5,6,1]=>{{1,4},{2,7},{3},{5,8},{6}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>[5,1,2,3,6,7,8,4]=>{{1,5,6,7,8},{2},{3},{4}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,4,8,1,7,5,6]=>[5,1,2,3,7,8,6,4]=>{{1,5,7},{2},{3},{4},{6,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>[5,1,2,3,8,4,6,7]=>{{1,5,8},{2},{3},{4},{6},{7}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,8,4,6,1,3,5,7]=>[5,1,6,3,7,4,8,2]=>{{1,5,7,8},{2},{3,6},{4}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,7,4,8,1,3,5,6]=>[5,1,6,3,7,8,2,4]=>{{1,5,7},{2},{3,6,8},{4}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,8,6,5,1,3,4,7]=>[5,1,6,7,4,3,8,2]=>{{1,5},{2},{3,6},{4,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,7,6,5,1,3,8,4]=>[5,1,6,8,4,3,2,7]=>{{1,5},{2},{3,6},{4,8},{7}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,8,4,5,1,7,3,6]=>[5,1,7,3,4,8,6,2]=>{{1,5},{2},{3,7},{4},{6,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,8,4,6,1,7,3,5]=>[5,1,7,3,8,4,6,2]=>{{1,5,8},{2},{3,7},{4},{6}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,3,4,8,1,2,5,6]=>[5,6,2,3,7,8,1,4]=>{{1,5,7},{2,6,8},{3},{4}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,3,8,5,1,2,4,6]=>[5,6,2,7,4,8,1,3]=>{{1,5},{2,6,8},{3},{4,7}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7,3,6,5,1,2,8,4]=>[5,6,2,8,4,3,1,7]=>{{1,5},{2,6},{3},{4,8},{7}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7,8,4,6,1,2,3,5]=>[5,6,7,3,8,4,1,2]=>{{1,5,8},{2,6},{3,7},{4}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2]=>{{1,5},{2,6},{3,7},{4,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8,3,6,5,1,7,2,4]=>[5,7,2,8,4,3,6,1]=>{{1,5},{2,7},{3},{4,8},{6}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>[6,1,2,3,4,7,8,5]=>{{1,6,7,8},{2},{3},{4},{5}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,3,4,8,6,1,5,7]=>[6,1,2,3,7,5,8,4]=>{{1,6},{2},{3},{4},{5,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[6,7,2,3,4,5,8,1]=>{{1,6},{2,7,8},{3},{4},{5}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8,3,4,5,7,1,2,6]=>[6,7,2,3,4,8,5,1]=>{{1,6,8},{2,7},{3},{4},{5}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>{{1,6},{2,7},{3,8},{4},{5}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>[7,1,2,3,4,5,8,6]=>{{1,7,8},{2},{3},{4},{5},{6}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,8,6,7,1,5]=>[7,1,2,3,8,5,6,4]=>{{1,7},{2},{3},{4},{5,8},{6}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[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]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,9},{8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,1,2,3,9,4,5,6,7]=>[2,3,4,6,7,8,9,1,5]=>{{1,2,3,4,6,8},{5,7,9}}
[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]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,4,6,8,9},{3},{5},{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]=>[2,9,1,3,4,5,6,7,8]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[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]=>[3,1,4,5,6,7,8,9,2]=>{{1,3,4,5,6,7,8,9},{2}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,9,1]=>{{1,3},{2,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2]=>{{1,3,5,7,9},{2,4,6,8}}
[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]=>[6,1,2,3,4,7,8,9,5]=>{{1,6,7,8,9},{2},{3},{4},{5}}
[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]=>[7,1,2,3,4,5,8,9,6]=>{{1,7,8,9},{2},{3},{4},{5},{6}}
[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]=>[8,1,2,3,4,5,6,9,7]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[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]=>[9,1,2,3,4,5,6,7,8]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[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]=>[9,1,2,3,4,5,6,7,10,8]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{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]=>[2,10,1,3,4,5,6,7,8,9]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[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]=>[10,1,2,3,4,5,6,7,8,11,9]=>{{1,10,11},{2},{3},{4},{5},{6},{7},{8},{9}}
[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]=>[8,1,2,3,4,5,6,9,10,7]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[]=>[1]=>[1]=>{{1}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10,3,1,5,2,7,4,9,6,8]=>[3,5,2,7,4,9,6,10,8,1]=>{{1,3},{2,5},{4,7},{6,9},{8,10}}
[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]=>[10,1,2,3,4,5,6,7,8,9]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[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]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[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]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,10},{9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,1,2,3,4,10,5,6,7,8]=>[2,3,4,5,7,8,9,10,1,6]=>{{1,2,3,4,5,7,9},{6,8,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[2,4,5,6,7,8,9,10,1,3]=>{{1,2,4,6,8,10},{3,5,7,9}}
[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]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[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]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,11},{10}}
[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]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[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]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}
[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]=>[3,1,4,5,6,7,8,9,10,2]=>{{1,3,4,5,6,7,8,9,10},{2}}
[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]=>[3,1,4,5,6,7,8,9,10,11,2]=>{{1,3,4,5,6,7,8,9,10,11},{2}}
[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]=>[11,1,2,3,4,5,6,7,8,9,10]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
inverse
Description
Sends a permutation to its inverse.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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