Identifier
Mp00041:
Integer compositions
—conjugate⟶
Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Images
=>
Cc0028;cc-rep-2Cc0002;cc-rep-3
[1]=>[1]=>[[1],[]]=>[1]
[1,1]=>[2]=>[[2],[]]=>[2]
[2]=>[1,1]=>[[1,1],[]]=>[1,1]
[1,1,1]=>[3]=>[[3],[]]=>[3]
[1,2]=>[1,2]=>[[2,1],[]]=>[2,1]
[2,1]=>[2,1]=>[[2,2],[1]]=>[2,2]
[3]=>[1,1,1]=>[[1,1,1],[]]=>[1,1,1]
[1,1,1,1]=>[4]=>[[4],[]]=>[4]
[1,1,2]=>[1,3]=>[[3,1],[]]=>[3,1]
[1,2,1]=>[2,2]=>[[3,2],[1]]=>[3,2]
[1,3]=>[1,1,2]=>[[2,1,1],[]]=>[2,1,1]
[2,1,1]=>[3,1]=>[[3,3],[2]]=>[3,3]
[2,2]=>[1,2,1]=>[[2,2,1],[1]]=>[2,2,1]
[3,1]=>[2,1,1]=>[[2,2,2],[1,1]]=>[2,2,2]
[4]=>[1,1,1,1]=>[[1,1,1,1],[]]=>[1,1,1,1]
[1,1,1,1,1]=>[5]=>[[5],[]]=>[5]
[1,1,1,2]=>[1,4]=>[[4,1],[]]=>[4,1]
[1,1,2,1]=>[2,3]=>[[4,2],[1]]=>[4,2]
[1,1,3]=>[1,1,3]=>[[3,1,1],[]]=>[3,1,1]
[1,2,1,1]=>[3,2]=>[[4,3],[2]]=>[4,3]
[1,2,2]=>[1,2,2]=>[[3,2,1],[1]]=>[3,2,1]
[1,3,1]=>[2,1,2]=>[[3,2,2],[1,1]]=>[3,2,2]
[1,4]=>[1,1,1,2]=>[[2,1,1,1],[]]=>[2,1,1,1]
[2,1,1,1]=>[4,1]=>[[4,4],[3]]=>[4,4]
[2,1,2]=>[1,3,1]=>[[3,3,1],[2]]=>[3,3,1]
[2,2,1]=>[2,2,1]=>[[3,3,2],[2,1]]=>[3,3,2]
[2,3]=>[1,1,2,1]=>[[2,2,1,1],[1]]=>[2,2,1,1]
[3,1,1]=>[3,1,1]=>[[3,3,3],[2,2]]=>[3,3,3]
[3,2]=>[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[2,2,2,1]
[4,1]=>[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[2,2,2,2]
[5]=>[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>[1,1,1,1,1]
[1,1,1,1,1,1]=>[6]=>[[6],[]]=>[6]
[1,1,1,1,2]=>[1,5]=>[[5,1],[]]=>[5,1]
[1,1,1,2,1]=>[2,4]=>[[5,2],[1]]=>[5,2]
[1,1,1,3]=>[1,1,4]=>[[4,1,1],[]]=>[4,1,1]
[1,1,2,1,1]=>[3,3]=>[[5,3],[2]]=>[5,3]
[1,1,2,2]=>[1,2,3]=>[[4,2,1],[1]]=>[4,2,1]
[1,1,3,1]=>[2,1,3]=>[[4,2,2],[1,1]]=>[4,2,2]
[1,1,4]=>[1,1,1,3]=>[[3,1,1,1],[]]=>[3,1,1,1]
[1,2,1,1,1]=>[4,2]=>[[5,4],[3]]=>[5,4]
[1,2,1,2]=>[1,3,2]=>[[4,3,1],[2]]=>[4,3,1]
[1,2,2,1]=>[2,2,2]=>[[4,3,2],[2,1]]=>[4,3,2]
[1,2,3]=>[1,1,2,2]=>[[3,2,1,1],[1]]=>[3,2,1,1]
[1,3,1,1]=>[3,1,2]=>[[4,3,3],[2,2]]=>[4,3,3]
[1,3,2]=>[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[3,2,2,1]
[1,4,1]=>[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[3,2,2,2]
[1,5]=>[1,1,1,1,2]=>[[2,1,1,1,1],[]]=>[2,1,1,1,1]
[2,1,1,1,1]=>[5,1]=>[[5,5],[4]]=>[5,5]
[2,1,1,2]=>[1,4,1]=>[[4,4,1],[3]]=>[4,4,1]
[2,1,2,1]=>[2,3,1]=>[[4,4,2],[3,1]]=>[4,4,2]
[2,1,3]=>[1,1,3,1]=>[[3,3,1,1],[2]]=>[3,3,1,1]
[2,2,1,1]=>[3,2,1]=>[[4,4,3],[3,2]]=>[4,4,3]
[2,2,2]=>[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[3,3,2,1]
[2,3,1]=>[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[3,3,2,2]
[2,4]=>[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[2,2,1,1,1]
[3,1,1,1]=>[4,1,1]=>[[4,4,4],[3,3]]=>[4,4,4]
[3,1,2]=>[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[3,3,3,1]
[3,2,1]=>[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[3,3,3,2]
[3,3]=>[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[2,2,2,1,1]
[4,1,1]=>[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[3,3,3,3]
[4,2]=>[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[2,2,2,2,1]
[5,1]=>[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[2,2,2,2,2]
[6]=>[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,1]=>[7]=>[[7],[]]=>[7]
[1,1,1,1,1,2]=>[1,6]=>[[6,1],[]]=>[6,1]
[1,1,1,1,2,1]=>[2,5]=>[[6,2],[1]]=>[6,2]
[1,1,1,1,3]=>[1,1,5]=>[[5,1,1],[]]=>[5,1,1]
[1,1,1,2,1,1]=>[3,4]=>[[6,3],[2]]=>[6,3]
[1,1,1,2,2]=>[1,2,4]=>[[5,2,1],[1]]=>[5,2,1]
[1,1,1,3,1]=>[2,1,4]=>[[5,2,2],[1,1]]=>[5,2,2]
[1,1,1,4]=>[1,1,1,4]=>[[4,1,1,1],[]]=>[4,1,1,1]
[1,1,2,1,1,1]=>[4,3]=>[[6,4],[3]]=>[6,4]
[1,1,2,1,2]=>[1,3,3]=>[[5,3,1],[2]]=>[5,3,1]
[1,1,2,2,1]=>[2,2,3]=>[[5,3,2],[2,1]]=>[5,3,2]
[1,1,2,3]=>[1,1,2,3]=>[[4,2,1,1],[1]]=>[4,2,1,1]
[1,1,3,1,1]=>[3,1,3]=>[[5,3,3],[2,2]]=>[5,3,3]
[1,1,3,2]=>[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[4,2,2,1]
[1,1,4,1]=>[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[4,2,2,2]
[1,1,5]=>[1,1,1,1,3]=>[[3,1,1,1,1],[]]=>[3,1,1,1,1]
[1,2,1,1,1,1]=>[5,2]=>[[6,5],[4]]=>[6,5]
[1,2,1,1,2]=>[1,4,2]=>[[5,4,1],[3]]=>[5,4,1]
[1,2,1,2,1]=>[2,3,2]=>[[5,4,2],[3,1]]=>[5,4,2]
[1,2,1,3]=>[1,1,3,2]=>[[4,3,1,1],[2]]=>[4,3,1,1]
[1,2,2,1,1]=>[3,2,2]=>[[5,4,3],[3,2]]=>[5,4,3]
[1,2,2,2]=>[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[4,3,2,1]
[1,2,3,1]=>[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[4,3,2,2]
[1,2,4]=>[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[3,2,1,1,1]
[1,3,1,1,1]=>[4,1,2]=>[[5,4,4],[3,3]]=>[5,4,4]
[1,3,1,2]=>[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[4,3,3,1]
[1,3,2,1]=>[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[4,3,3,2]
[1,3,3]=>[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[3,2,2,1,1]
[1,4,1,1]=>[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[4,3,3,3]
[1,4,2]=>[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[3,2,2,2,1]
[1,5,1]=>[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[3,2,2,2,2]
[1,6]=>[1,1,1,1,1,2]=>[[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1]
[2,1,1,1,1,1]=>[6,1]=>[[6,6],[5]]=>[6,6]
[2,1,1,1,2]=>[1,5,1]=>[[5,5,1],[4]]=>[5,5,1]
[2,1,1,2,1]=>[2,4,1]=>[[5,5,2],[4,1]]=>[5,5,2]
[2,1,1,3]=>[1,1,4,1]=>[[4,4,1,1],[3]]=>[4,4,1,1]
[2,1,2,1,1]=>[3,3,1]=>[[5,5,3],[4,2]]=>[5,5,3]
[2,1,2,2]=>[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[4,4,2,1]
[2,1,3,1]=>[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[4,4,2,2]
[2,1,4]=>[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[3,3,1,1,1]
[2,2,1,1,1]=>[4,2,1]=>[[5,5,4],[4,3]]=>[5,5,4]
[2,2,1,2]=>[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[4,4,3,1]
[2,2,2,1]=>[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[4,4,3,2]
[2,2,3]=>[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[3,3,2,1,1]
[2,3,1,1]=>[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[4,4,3,3]
[2,3,2]=>[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[3,3,2,2,1]
[2,4,1]=>[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[3,3,2,2,2]
[2,5]=>[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[2,2,1,1,1,1]
[3,1,1,1,1]=>[5,1,1]=>[[5,5,5],[4,4]]=>[5,5,5]
[3,1,1,2]=>[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[4,4,4,1]
[3,1,2,1]=>[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[4,4,4,2]
[3,1,3]=>[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[3,3,3,1,1]
[3,2,1,1]=>[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[4,4,4,3]
[3,2,2]=>[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[3,3,3,2,1]
[3,3,1]=>[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[3,3,3,2,2]
[3,4]=>[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[2,2,2,1,1,1]
[4,1,1,1]=>[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[4,4,4,4]
[4,1,2]=>[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[3,3,3,3,1]
[4,2,1]=>[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[3,3,3,3,2]
[4,3]=>[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[2,2,2,2,1,1]
[5,1,1]=>[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[3,3,3,3,3]
[5,2]=>[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[2,2,2,2,2,1]
[6,1]=>[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[2,2,2,2,2,2]
[7]=>[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1]=>[8]=>[[8],[]]=>[8]
[1,1,1,1,1,1,2]=>[1,7]=>[[7,1],[]]=>[7,1]
[1,1,1,1,1,3]=>[1,1,6]=>[[6,1,1],[]]=>[6,1,1]
[1,1,1,1,4]=>[1,1,1,5]=>[[5,1,1,1],[]]=>[5,1,1,1]
[1,1,1,2,1,1,1]=>[4,4]=>[[7,4],[3]]=>[7,4]
[1,1,1,5]=>[1,1,1,1,4]=>[[4,1,1,1,1],[]]=>[4,1,1,1,1]
[1,1,2,1,1,2]=>[1,4,3]=>[[6,4,1],[3]]=>[6,4,1]
[1,1,2,1,2,1]=>[2,3,3]=>[[6,4,2],[3,1]]=>[6,4,2]
[1,1,2,1,3]=>[1,1,3,3]=>[[5,3,1,1],[2]]=>[5,3,1,1]
[1,1,2,2,1,1]=>[3,2,3]=>[[6,4,3],[3,2]]=>[6,4,3]
[1,1,2,2,2]=>[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[5,3,2,1]
[1,1,2,3,1]=>[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[5,3,2,2]
[1,1,3,1,1,1]=>[4,1,3]=>[[6,4,4],[3,3]]=>[6,4,4]
[1,1,3,1,2]=>[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[5,3,3,1]
[1,1,3,2,1]=>[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[5,3,3,2]
[1,1,4,1,1]=>[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[5,3,3,3]
[1,1,6]=>[1,1,1,1,1,3]=>[[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1]
[1,2,1,1,2,1]=>[2,4,2]=>[[6,5,2],[4,1]]=>[6,5,2]
[1,2,1,2,1,1]=>[3,3,2]=>[[6,5,3],[4,2]]=>[6,5,3]
[1,2,1,2,2]=>[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[5,4,2,1]
[1,2,1,3,1]=>[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[5,4,2,2]
[1,2,1,4]=>[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[4,3,1,1,1]
[1,2,2,1,1,1]=>[4,2,2]=>[[6,5,4],[4,3]]=>[6,5,4]
[1,2,2,1,2]=>[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[5,4,3,1]
[1,2,2,2,1]=>[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[5,4,3,2]
[1,2,2,3]=>[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[4,3,2,1,1]
[1,2,3,1,1]=>[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[5,4,3,3]
[1,2,3,2]=>[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[4,3,2,2,1]
[1,2,4,1]=>[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[4,3,2,2,2]
[1,2,5]=>[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[3,2,1,1,1,1]
[1,3,1,1,2]=>[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[5,4,4,1]
[1,3,1,2,1]=>[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[5,4,4,2]
[1,3,1,3]=>[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[4,3,3,1,1]
[1,3,2,1,1]=>[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[5,4,4,3]
[1,3,2,2]=>[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[4,3,3,2,1]
[1,3,3,1]=>[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[4,3,3,2,2]
[1,3,4]=>[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[3,2,2,1,1,1]
[1,4,1,1,1]=>[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[5,4,4,4]
[1,4,1,2]=>[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[4,3,3,3,1]
[1,4,2,1]=>[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[4,3,3,3,2]
[1,4,3]=>[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[3,2,2,2,1,1]
[1,5,2]=>[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[3,2,2,2,2,1]
[1,6,1]=>[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[3,2,2,2,2,2]
[1,7]=>[1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1]
[2,1,1,1,1,1,1]=>[7,1]=>[[7,7],[6]]=>[7,7]
[2,1,1,2,1,1]=>[3,4,1]=>[[6,6,3],[5,2]]=>[6,6,3]
[2,1,2,1,1,1]=>[4,3,1]=>[[6,6,4],[5,3]]=>[6,6,4]
[2,1,2,1,2]=>[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[5,5,3,1]
[2,1,2,2,1]=>[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[5,5,3,2]
[2,1,2,3]=>[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[4,4,2,1,1]
[2,1,3,1,1]=>[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[5,5,3,3]
[2,1,3,2]=>[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[4,4,2,2,1]
[2,1,4,1]=>[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[4,4,2,2,2]
[2,2,1,1,2]=>[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[5,5,4,1]
[2,2,1,2,1]=>[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[5,5,4,2]
[2,2,1,3]=>[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[4,4,3,1,1]
[2,2,2,1,1]=>[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[5,5,4,3]
[2,2,2,2]=>[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[4,4,3,2,1]
[2,2,3,1]=>[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[4,4,3,2,2]
[2,2,4]=>[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[3,3,2,1,1,1]
[2,3,1,1,1]=>[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[5,5,4,4]
[2,3,1,2]=>[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[4,4,3,3,1]
[2,3,2,1]=>[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[4,4,3,3,2]
[2,3,3]=>[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[3,3,2,2,1,1]
[2,4,1,1]=>[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[4,4,3,3,3]
[2,4,2]=>[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[3,3,2,2,2,1]
[2,5,1]=>[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[3,3,2,2,2,2]
[2,6]=>[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[2,2,1,1,1,1,1]
[3,1,1,1,1,1]=>[6,1,1]=>[[6,6,6],[5,5]]=>[6,6,6]
[3,1,1,2,1]=>[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[5,5,5,2]
[3,1,2,1,1]=>[3,3,1,1]=>[[5,5,5,3],[4,4,2]]=>[5,5,5,3]
[3,1,2,2]=>[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[4,4,4,2,1]
[3,1,3,1]=>[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[4,4,4,2,2]
[3,2,1,1,1]=>[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[5,5,5,4]
[3,2,1,2]=>[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[4,4,4,3,1]
[3,2,2,1]=>[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[4,4,4,3,2]
[3,2,3]=>[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[3,3,3,2,1,1]
[3,3,1,1]=>[3,1,2,1,1]=>[[4,4,4,3,3],[3,3,2,2]]=>[4,4,4,3,3]
[3,3,2]=>[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[3,3,3,2,2,1]
[3,4,1]=>[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[3,3,3,2,2,2]
[3,5]=>[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[2,2,2,1,1,1,1]
[4,1,1,1,1]=>[5,1,1,1]=>[[5,5,5,5],[4,4,4]]=>[5,5,5,5]
[4,1,1,2]=>[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[4,4,4,4,1]
[4,1,2,1]=>[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[4,4,4,4,2]
[4,2,1,1]=>[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[4,4,4,4,3]
[4,2,2]=>[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[3,3,3,3,2,1]
[4,3,1]=>[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[3,3,3,3,2,2]
[4,4]=>[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[2,2,2,2,1,1,1]
[5,1,1,1]=>[4,1,1,1,1]=>[[4,4,4,4,4],[3,3,3,3]]=>[4,4,4,4,4]
[5,2,1]=>[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[3,3,3,3,3,2]
[5,3]=>[1,1,2,1,1,1,1]=>[[2,2,2,2,2,1,1],[1,1,1,1]]=>[2,2,2,2,2,1,1]
[6,1,1]=>[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[3,3,3,3,3,3]
[6,2]=>[1,2,1,1,1,1,1]=>[[2,2,2,2,2,2,1],[1,1,1,1,1]]=>[2,2,2,2,2,2,1]
[7,1]=>[2,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2],[1,1,1,1,1,1]]=>[2,2,2,2,2,2,2]
[8]=>[1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1]=>[9]=>[[9],[]]=>[9]
[1,1,1,1,1,1,1,2]=>[1,8]=>[[8,1],[]]=>[8,1]
[1,1,1,1,1,1,3]=>[1,1,7]=>[[7,1,1],[]]=>[7,1,1]
[1,1,1,1,1,4]=>[1,1,1,6]=>[[6,1,1,1],[]]=>[6,1,1,1]
[1,1,1,1,5]=>[1,1,1,1,5]=>[[5,1,1,1,1],[]]=>[5,1,1,1,1]
[1,1,1,6]=>[1,1,1,1,1,4]=>[[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1]
[1,1,7]=>[1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1]
[1,8]=>[1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1]=>[8,1]=>[[8,8],[7]]=>[8,8]
[3,1,1,1,1,1,1]=>[7,1,1]=>[[7,7,7],[6,6]]=>[7,7,7]
[4,1,1,1,1,1]=>[6,1,1,1]=>[[6,6,6,6],[5,5,5]]=>[6,6,6,6]
[5,1,1,1,1]=>[5,1,1,1,1]=>[[5,5,5,5,5],[4,4,4,4]]=>[5,5,5,5,5]
[6,1,1,1]=>[4,1,1,1,1,1]=>[[4,4,4,4,4,4],[3,3,3,3,3]]=>[4,4,4,4,4,4]
[7,1,1]=>[3,1,1,1,1,1,1]=>[[3,3,3,3,3,3,3],[2,2,2,2,2,2]]=>[3,3,3,3,3,3,3]
[8,1]=>[2,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]=>[2,2,2,2,2,2,2,2]
[9]=>[1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1]=>[10]=>[[10],[]]=>[10]
[1,1,1,1,1,1,1,1,2]=>[1,9]=>[[9,1],[]]=>[9,1]
[1,1,1,1,1,1,1,3]=>[1,1,8]=>[[8,1,1],[]]=>[8,1,1]
[1,1,1,1,1,1,4]=>[1,1,1,7]=>[[7,1,1,1],[]]=>[7,1,1,1]
[1,1,1,1,1,5]=>[1,1,1,1,6]=>[[6,1,1,1,1],[]]=>[6,1,1,1,1]
[1,1,1,1,6]=>[1,1,1,1,1,5]=>[[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1]
[1,1,1,7]=>[1,1,1,1,1,1,4]=>[[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1]
[1,1,8]=>[1,1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1]
[1,9]=>[1,1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1]=>[9,1]=>[[9,9],[8]]=>[9,9]
[3,1,1,1,1,1,1,1]=>[8,1,1]=>[[8,8,8],[7,7]]=>[8,8,8]
[4,1,1,1,1,1,1]=>[7,1,1,1]=>[[7,7,7,7],[6,6,6]]=>[7,7,7,7]
[5,1,1,1,1,1]=>[6,1,1,1,1]=>[[6,6,6,6,6],[5,5,5,5]]=>[6,6,6,6,6]
[6,1,1,1,1]=>[5,1,1,1,1,1]=>[[5,5,5,5,5,5],[4,4,4,4,4]]=>[5,5,5,5,5,5]
[7,1,1,1]=>[4,1,1,1,1,1,1]=>[[4,4,4,4,4,4,4],[3,3,3,3,3,3]]=>[4,4,4,4,4,4,4]
[8,1,1]=>[3,1,1,1,1,1,1,1]=>[[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]=>[3,3,3,3,3,3,3,3]
[9,1]=>[2,1,1,1,1,1,1,1,1]=>[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]=>[2,2,2,2,2,2,2,2,2]
[10]=>[1,1,1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1,1,1]
Map
conjugate
Description
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
outer shape
Description
The outer shape of the skew partition.
searching the database
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