Identifier
Mp00180:
Integer compositions
—to ribbon⟶
Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
=>
Cc0028;cc-rep-1Cc0002;cc-rep-2Cc0002;cc-rep-3
[1]=>[[1],[]]=>[1]=>[1]
[1,1]=>[[1,1],[]]=>[1,1]=>[2]
[2]=>[[2],[]]=>[2]=>[1,1]
[1,1,1]=>[[1,1,1],[]]=>[1,1,1]=>[3]
[1,2]=>[[2,1],[]]=>[2,1]=>[2,1]
[2,1]=>[[2,2],[1]]=>[2,2]=>[2,2]
[3]=>[[3],[]]=>[3]=>[1,1,1]
[1,1,1,1]=>[[1,1,1,1],[]]=>[1,1,1,1]=>[4]
[1,1,2]=>[[2,1,1],[]]=>[2,1,1]=>[3,1]
[1,2,1]=>[[2,2,1],[1]]=>[2,2,1]=>[3,2]
[1,3]=>[[3,1],[]]=>[3,1]=>[2,1,1]
[2,1,1]=>[[2,2,2],[1,1]]=>[2,2,2]=>[3,3]
[2,2]=>[[3,2],[1]]=>[3,2]=>[2,2,1]
[3,1]=>[[3,3],[2]]=>[3,3]=>[2,2,2]
[4]=>[[4],[]]=>[4]=>[1,1,1,1]
[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>[1,1,1,1,1]=>[5]
[1,1,1,2]=>[[2,1,1,1],[]]=>[2,1,1,1]=>[4,1]
[1,1,2,1]=>[[2,2,1,1],[1]]=>[2,2,1,1]=>[4,2]
[1,1,3]=>[[3,1,1],[]]=>[3,1,1]=>[3,1,1]
[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[2,2,2,1]=>[4,3]
[1,2,2]=>[[3,2,1],[1]]=>[3,2,1]=>[3,2,1]
[1,3,1]=>[[3,3,1],[2]]=>[3,3,1]=>[3,2,2]
[1,4]=>[[4,1],[]]=>[4,1]=>[2,1,1,1]
[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[2,2,2,2]=>[4,4]
[2,1,2]=>[[3,2,2],[1,1]]=>[3,2,2]=>[3,3,1]
[2,2,1]=>[[3,3,2],[2,1]]=>[3,3,2]=>[3,3,2]
[2,3]=>[[4,2],[1]]=>[4,2]=>[2,2,1,1]
[3,1,1]=>[[3,3,3],[2,2]]=>[3,3,3]=>[3,3,3]
[3,2]=>[[4,3],[2]]=>[4,3]=>[2,2,2,1]
[4,1]=>[[4,4],[3]]=>[4,4]=>[2,2,2,2]
[5]=>[[5],[]]=>[5]=>[1,1,1,1,1]
[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1]=>[6]
[1,1,1,1,2]=>[[2,1,1,1,1],[]]=>[2,1,1,1,1]=>[5,1]
[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[2,2,1,1,1]=>[5,2]
[1,1,1,3]=>[[3,1,1,1],[]]=>[3,1,1,1]=>[4,1,1]
[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[2,2,2,1,1]=>[5,3]
[1,1,2,2]=>[[3,2,1,1],[1]]=>[3,2,1,1]=>[4,2,1]
[1,1,3,1]=>[[3,3,1,1],[2]]=>[3,3,1,1]=>[4,2,2]
[1,1,4]=>[[4,1,1],[]]=>[4,1,1]=>[3,1,1,1]
[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[2,2,2,2,1]=>[5,4]
[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[3,2,2,1]=>[4,3,1]
[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[3,3,2,1]=>[4,3,2]
[1,2,3]=>[[4,2,1],[1]]=>[4,2,1]=>[3,2,1,1]
[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[3,3,3,1]=>[4,3,3]
[1,3,2]=>[[4,3,1],[2]]=>[4,3,1]=>[3,2,2,1]
[1,4,1]=>[[4,4,1],[3]]=>[4,4,1]=>[3,2,2,2]
[1,5]=>[[5,1],[]]=>[5,1]=>[2,1,1,1,1]
[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[2,2,2,2,2]=>[5,5]
[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[3,2,2,2]=>[4,4,1]
[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[3,3,2,2]=>[4,4,2]
[2,1,3]=>[[4,2,2],[1,1]]=>[4,2,2]=>[3,3,1,1]
[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[3,3,3,2]=>[4,4,3]
[2,2,2]=>[[4,3,2],[2,1]]=>[4,3,2]=>[3,3,2,1]
[2,3,1]=>[[4,4,2],[3,1]]=>[4,4,2]=>[3,3,2,2]
[2,4]=>[[5,2],[1]]=>[5,2]=>[2,2,1,1,1]
[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[3,3,3,3]=>[4,4,4]
[3,1,2]=>[[4,3,3],[2,2]]=>[4,3,3]=>[3,3,3,1]
[3,2,1]=>[[4,4,3],[3,2]]=>[4,4,3]=>[3,3,3,2]
[3,3]=>[[5,3],[2]]=>[5,3]=>[2,2,2,1,1]
[4,1,1]=>[[4,4,4],[3,3]]=>[4,4,4]=>[3,3,3,3]
[4,2]=>[[5,4],[3]]=>[5,4]=>[2,2,2,2,1]
[5,1]=>[[5,5],[4]]=>[5,5]=>[2,2,2,2,2]
[6]=>[[6],[]]=>[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1]=>[7]
[1,1,1,1,1,2]=>[[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1]=>[6,1]
[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[2,2,1,1,1,1]=>[6,2]
[1,1,1,1,3]=>[[3,1,1,1,1],[]]=>[3,1,1,1,1]=>[5,1,1]
[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[2,2,2,1,1,1]=>[6,3]
[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[3,2,1,1,1]=>[5,2,1]
[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[3,3,1,1,1]=>[5,2,2]
[1,1,1,4]=>[[4,1,1,1],[]]=>[4,1,1,1]=>[4,1,1,1]
[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[2,2,2,2,1,1]=>[6,4]
[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[3,2,2,1,1]=>[5,3,1]
[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[3,3,2,1,1]=>[5,3,2]
[1,1,2,3]=>[[4,2,1,1],[1]]=>[4,2,1,1]=>[4,2,1,1]
[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[3,3,3,1,1]=>[5,3,3]
[1,1,3,2]=>[[4,3,1,1],[2]]=>[4,3,1,1]=>[4,2,2,1]
[1,1,4,1]=>[[4,4,1,1],[3]]=>[4,4,1,1]=>[4,2,2,2]
[1,1,5]=>[[5,1,1],[]]=>[5,1,1]=>[3,1,1,1,1]
[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[2,2,2,2,2,1]=>[6,5]
[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[3,2,2,2,1]=>[5,4,1]
[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[3,3,2,2,1]=>[5,4,2]
[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[4,2,2,1]=>[4,3,1,1]
[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[3,3,3,2,1]=>[5,4,3]
[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[4,3,2,1]=>[4,3,2,1]
[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[4,4,2,1]=>[4,3,2,2]
[1,2,4]=>[[5,2,1],[1]]=>[5,2,1]=>[3,2,1,1,1]
[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[3,3,3,3,1]=>[5,4,4]
[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[4,3,3,1]=>[4,3,3,1]
[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[4,4,3,1]=>[4,3,3,2]
[1,3,3]=>[[5,3,1],[2]]=>[5,3,1]=>[3,2,2,1,1]
[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[4,4,4,1]=>[4,3,3,3]
[1,4,2]=>[[5,4,1],[3]]=>[5,4,1]=>[3,2,2,2,1]
[1,5,1]=>[[5,5,1],[4]]=>[5,5,1]=>[3,2,2,2,2]
[1,6]=>[[6,1],[]]=>[6,1]=>[2,1,1,1,1,1]
[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[2,2,2,2,2,2]=>[6,6]
[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[3,2,2,2,2]=>[5,5,1]
[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[3,3,2,2,2]=>[5,5,2]
[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[4,2,2,2]=>[4,4,1,1]
[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[3,3,3,2,2]=>[5,5,3]
[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[4,3,2,2]=>[4,4,2,1]
[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[4,4,2,2]=>[4,4,2,2]
[2,1,4]=>[[5,2,2],[1,1]]=>[5,2,2]=>[3,3,1,1,1]
[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[3,3,3,3,2]=>[5,5,4]
[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[4,3,3,2]=>[4,4,3,1]
[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[4,4,3,2]=>[4,4,3,2]
[2,2,3]=>[[5,3,2],[2,1]]=>[5,3,2]=>[3,3,2,1,1]
[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[4,4,4,2]=>[4,4,3,3]
[2,3,2]=>[[5,4,2],[3,1]]=>[5,4,2]=>[3,3,2,2,1]
[2,4,1]=>[[5,5,2],[4,1]]=>[5,5,2]=>[3,3,2,2,2]
[2,5]=>[[6,2],[1]]=>[6,2]=>[2,2,1,1,1,1]
[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[3,3,3,3,3]=>[5,5,5]
[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[4,3,3,3]=>[4,4,4,1]
[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[4,4,3,3]=>[4,4,4,2]
[3,1,3]=>[[5,3,3],[2,2]]=>[5,3,3]=>[3,3,3,1,1]
[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[4,4,4,3]=>[4,4,4,3]
[3,2,2]=>[[5,4,3],[3,2]]=>[5,4,3]=>[3,3,3,2,1]
[3,3,1]=>[[5,5,3],[4,2]]=>[5,5,3]=>[3,3,3,2,2]
[3,4]=>[[6,3],[2]]=>[6,3]=>[2,2,2,1,1,1]
[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[4,4,4,4]=>[4,4,4,4]
[4,1,2]=>[[5,4,4],[3,3]]=>[5,4,4]=>[3,3,3,3,1]
[4,2,1]=>[[5,5,4],[4,3]]=>[5,5,4]=>[3,3,3,3,2]
[4,3]=>[[6,4],[3]]=>[6,4]=>[2,2,2,2,1,1]
[5,1,1]=>[[5,5,5],[4,4]]=>[5,5,5]=>[3,3,3,3,3]
[5,2]=>[[6,5],[4]]=>[6,5]=>[2,2,2,2,2,1]
[6,1]=>[[6,6],[5]]=>[6,6]=>[2,2,2,2,2,2]
[7]=>[[7],[]]=>[7]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1,1]=>[8]
[1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1]=>[7,1]
[1,1,1,1,1,2,1]=>[[2,2,1,1,1,1,1],[1]]=>[2,2,1,1,1,1,1]=>[7,2]
[1,1,1,1,1,3]=>[[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1]=>[6,1,1]
[1,1,1,1,2,1,1]=>[[2,2,2,1,1,1,1],[1,1]]=>[2,2,2,1,1,1,1]=>[7,3]
[1,1,1,1,2,2]=>[[3,2,1,1,1,1],[1]]=>[3,2,1,1,1,1]=>[6,2,1]
[1,1,1,1,4]=>[[4,1,1,1,1],[]]=>[4,1,1,1,1]=>[5,1,1,1]
[1,1,1,2,1,1,1]=>[[2,2,2,2,1,1,1],[1,1,1]]=>[2,2,2,2,1,1,1]=>[7,4]
[1,1,1,2,1,2]=>[[3,2,2,1,1,1],[1,1]]=>[3,2,2,1,1,1]=>[6,3,1]
[1,1,1,2,2,1]=>[[3,3,2,1,1,1],[2,1]]=>[3,3,2,1,1,1]=>[6,3,2]
[1,1,1,3,2]=>[[4,3,1,1,1],[2]]=>[4,3,1,1,1]=>[5,2,2,1]
[1,1,1,5]=>[[5,1,1,1],[]]=>[5,1,1,1]=>[4,1,1,1,1]
[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]=>[7,5]
[1,1,2,1,1,2]=>[[3,2,2,2,1,1],[1,1,1]]=>[3,2,2,2,1,1]=>[6,4,1]
[1,1,2,1,2,1]=>[[3,3,2,2,1,1],[2,1,1]]=>[3,3,2,2,1,1]=>[6,4,2]
[1,1,2,2,1,1]=>[[3,3,3,2,1,1],[2,2,1]]=>[3,3,3,2,1,1]=>[6,4,3]
[1,1,2,2,2]=>[[4,3,2,1,1],[2,1]]=>[4,3,2,1,1]=>[5,3,2,1]
[1,1,2,3,1]=>[[4,4,2,1,1],[3,1]]=>[4,4,2,1,1]=>[5,3,2,2]
[1,1,3,1,2]=>[[4,3,3,1,1],[2,2]]=>[4,3,3,1,1]=>[5,3,3,1]
[1,1,3,2,1]=>[[4,4,3,1,1],[3,2]]=>[4,4,3,1,1]=>[5,3,3,2]
[1,1,3,3]=>[[5,3,1,1],[2]]=>[5,3,1,1]=>[4,2,2,1,1]
[1,1,6]=>[[6,1,1],[]]=>[6,1,1]=>[3,1,1,1,1,1]
[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]=>[7,6]
[1,2,1,1,1,2]=>[[3,2,2,2,2,1],[1,1,1,1]]=>[3,2,2,2,2,1]=>[6,5,1]
[1,2,1,1,2,1]=>[[3,3,2,2,2,1],[2,1,1,1]]=>[3,3,2,2,2,1]=>[6,5,2]
[1,2,1,2,1,1]=>[[3,3,3,2,2,1],[2,2,1,1]]=>[3,3,3,2,2,1]=>[6,5,3]
[1,2,1,2,2]=>[[4,3,2,2,1],[2,1,1]]=>[4,3,2,2,1]=>[5,4,2,1]
[1,2,1,3,1]=>[[4,4,2,2,1],[3,1,1]]=>[4,4,2,2,1]=>[5,4,2,2]
[1,2,2,1,1,1]=>[[3,3,3,3,2,1],[2,2,2,1]]=>[3,3,3,3,2,1]=>[6,5,4]
[1,2,2,1,2]=>[[4,3,3,2,1],[2,2,1]]=>[4,3,3,2,1]=>[5,4,3,1]
[1,2,2,2,1]=>[[4,4,3,2,1],[3,2,1]]=>[4,4,3,2,1]=>[5,4,3,2]
[1,2,2,3]=>[[5,3,2,1],[2,1]]=>[5,3,2,1]=>[4,3,2,1,1]
[1,2,3,1,1]=>[[4,4,4,2,1],[3,3,1]]=>[4,4,4,2,1]=>[5,4,3,3]
[1,2,3,2]=>[[5,4,2,1],[3,1]]=>[5,4,2,1]=>[4,3,2,2,1]
[1,3,1,1,2]=>[[4,3,3,3,1],[2,2,2]]=>[4,3,3,3,1]=>[5,4,4,1]
[1,3,1,2,1]=>[[4,4,3,3,1],[3,2,2]]=>[4,4,3,3,1]=>[5,4,4,2]
[1,3,1,3]=>[[5,3,3,1],[2,2]]=>[5,3,3,1]=>[4,3,3,1,1]
[1,3,2,1,1]=>[[4,4,4,3,1],[3,3,2]]=>[4,4,4,3,1]=>[5,4,4,3]
[1,3,2,2]=>[[5,4,3,1],[3,2]]=>[5,4,3,1]=>[4,3,3,2,1]
[1,3,3,1]=>[[5,5,3,1],[4,2]]=>[5,5,3,1]=>[4,3,3,2,2]
[1,4,1,1,1]=>[[4,4,4,4,1],[3,3,3]]=>[4,4,4,4,1]=>[5,4,4,4]
[1,4,1,2]=>[[5,4,4,1],[3,3]]=>[5,4,4,1]=>[4,3,3,3,1]
[1,4,2,1]=>[[5,5,4,1],[4,3]]=>[5,5,4,1]=>[4,3,3,3,2]
[1,4,3]=>[[6,4,1],[3]]=>[6,4,1]=>[3,2,2,2,1,1]
[1,7]=>[[7,1],[]]=>[7,1]=>[2,1,1,1,1,1,1]
[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]=>[7,7]
[2,1,1,1,1,2]=>[[3,2,2,2,2,2],[1,1,1,1,1]]=>[3,2,2,2,2,2]=>[6,6,1]
[2,1,1,1,2,1]=>[[3,3,2,2,2,2],[2,1,1,1,1]]=>[3,3,2,2,2,2]=>[6,6,2]
[2,1,1,2,1,1]=>[[3,3,3,2,2,2],[2,2,1,1,1]]=>[3,3,3,2,2,2]=>[6,6,3]
[2,1,1,2,2]=>[[4,3,2,2,2],[2,1,1,1]]=>[4,3,2,2,2]=>[5,5,2,1]
[2,1,1,3,1]=>[[4,4,2,2,2],[3,1,1,1]]=>[4,4,2,2,2]=>[5,5,2,2]
[2,1,2,1,1,1]=>[[3,3,3,3,2,2],[2,2,2,1,1]]=>[3,3,3,3,2,2]=>[6,6,4]
[2,1,2,1,2]=>[[4,3,3,2,2],[2,2,1,1]]=>[4,3,3,2,2]=>[5,5,3,1]
[2,1,2,2,1]=>[[4,4,3,2,2],[3,2,1,1]]=>[4,4,3,2,2]=>[5,5,3,2]
[2,1,2,3]=>[[5,3,2,2],[2,1,1]]=>[5,3,2,2]=>[4,4,2,1,1]
[2,1,3,1,1]=>[[4,4,4,2,2],[3,3,1,1]]=>[4,4,4,2,2]=>[5,5,3,3]
[2,1,3,2]=>[[5,4,2,2],[3,1,1]]=>[5,4,2,2]=>[4,4,2,2,1]
[2,2,1,1,1,1]=>[[3,3,3,3,3,2],[2,2,2,2,1]]=>[3,3,3,3,3,2]=>[6,6,5]
[2,2,1,1,2]=>[[4,3,3,3,2],[2,2,2,1]]=>[4,3,3,3,2]=>[5,5,4,1]
[2,2,1,2,1]=>[[4,4,3,3,2],[3,2,2,1]]=>[4,4,3,3,2]=>[5,5,4,2]
[2,2,1,3]=>[[5,3,3,2],[2,2,1]]=>[5,3,3,2]=>[4,4,3,1,1]
[2,2,2,1,1]=>[[4,4,4,3,2],[3,3,2,1]]=>[4,4,4,3,2]=>[5,5,4,3]
[2,2,2,2]=>[[5,4,3,2],[3,2,1]]=>[5,4,3,2]=>[4,4,3,2,1]
[2,2,3,1]=>[[5,5,3,2],[4,2,1]]=>[5,5,3,2]=>[4,4,3,2,2]
[2,3,1,1,1]=>[[4,4,4,4,2],[3,3,3,1]]=>[4,4,4,4,2]=>[5,5,4,4]
[2,3,1,2]=>[[5,4,4,2],[3,3,1]]=>[5,4,4,2]=>[4,4,3,3,1]
[2,3,2,1]=>[[5,5,4,2],[4,3,1]]=>[5,5,4,2]=>[4,4,3,3,2]
[2,3,3]=>[[6,4,2],[3,1]]=>[6,4,2]=>[3,3,2,2,1,1]
[2,4,1,1]=>[[5,5,5,2],[4,4,1]]=>[5,5,5,2]=>[4,4,3,3,3]
[2,4,2]=>[[6,5,2],[4,1]]=>[6,5,2]=>[3,3,2,2,2,1]
[3,1,1,1,1,1]=>[[3,3,3,3,3,3],[2,2,2,2,2]]=>[3,3,3,3,3,3]=>[6,6,6]
[3,1,1,2,1]=>[[4,4,3,3,3],[3,2,2,2]]=>[4,4,3,3,3]=>[5,5,5,2]
[3,1,1,3]=>[[5,3,3,3],[2,2,2]]=>[5,3,3,3]=>[4,4,4,1,1]
[3,1,2,2]=>[[5,4,3,3],[3,2,2]]=>[5,4,3,3]=>[4,4,4,2,1]
[3,1,3,1]=>[[5,5,3,3],[4,2,2]]=>[5,5,3,3]=>[4,4,4,2,2]
[3,2,1,1,1]=>[[4,4,4,4,3],[3,3,3,2]]=>[4,4,4,4,3]=>[5,5,5,4]
[3,2,1,2]=>[[5,4,4,3],[3,3,2]]=>[5,4,4,3]=>[4,4,4,3,1]
[3,2,2,1]=>[[5,5,4,3],[4,3,2]]=>[5,5,4,3]=>[4,4,4,3,2]
[3,2,3]=>[[6,4,3],[3,2]]=>[6,4,3]=>[3,3,3,2,1,1]
[3,3,2]=>[[6,5,3],[4,2]]=>[6,5,3]=>[3,3,3,2,2,1]
[3,4,1]=>[[6,6,3],[5,2]]=>[6,6,3]=>[3,3,3,2,2,2]
[4,1,1,1,1]=>[[4,4,4,4,4],[3,3,3,3]]=>[4,4,4,4,4]=>[5,5,5,5]
[4,1,1,2]=>[[5,4,4,4],[3,3,3]]=>[5,4,4,4]=>[4,4,4,4,1]
[4,1,2,1]=>[[5,5,4,4],[4,3,3]]=>[5,5,4,4]=>[4,4,4,4,2]
[4,1,3]=>[[6,4,4],[3,3]]=>[6,4,4]=>[3,3,3,3,1,1]
[4,2,1,1]=>[[5,5,5,4],[4,4,3]]=>[5,5,5,4]=>[4,4,4,4,3]
[4,2,2]=>[[6,5,4],[4,3]]=>[6,5,4]=>[3,3,3,3,2,1]
[4,3,1]=>[[6,6,4],[5,3]]=>[6,6,4]=>[3,3,3,3,2,2]
[4,4]=>[[7,4],[3]]=>[7,4]=>[2,2,2,2,1,1,1]
[5,1,1,1]=>[[5,5,5,5],[4,4,4]]=>[5,5,5,5]=>[4,4,4,4,4]
[6,1,1]=>[[6,6,6],[5,5]]=>[6,6,6]=>[3,3,3,3,3,3]
[7,1]=>[[7,7],[6]]=>[7,7]=>[2,2,2,2,2,2,2]
[8]=>[[8],[]]=>[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],[]]=>[1,1,1,1,1,1,1,1,1]=>[9]
[1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1]=>[8,1]
[1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1]=>[7,1,1]
[1,1,1,1,1,4]=>[[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1]=>[6,1,1,1]
[1,1,1,1,5]=>[[5,1,1,1,1],[]]=>[5,1,1,1,1]=>[5,1,1,1,1]
[1,1,1,6]=>[[6,1,1,1],[]]=>[6,1,1,1]=>[4,1,1,1,1,1]
[1,1,7]=>[[7,1,1],[]]=>[7,1,1]=>[3,1,1,1,1,1,1]
[1,8]=>[[8,1],[]]=>[8,1]=>[2,1,1,1,1,1,1,1]
[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]=>[8,8]
[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]=>[7,7,7]
[4,1,1,1,1,1]=>[[4,4,4,4,4,4],[3,3,3,3,3]]=>[4,4,4,4,4,4]=>[6,6,6,6]
[5,1,1,1,1]=>[[5,5,5,5,5],[4,4,4,4]]=>[5,5,5,5,5]=>[5,5,5,5,5]
[6,1,1,1]=>[[6,6,6,6],[5,5,5]]=>[6,6,6,6]=>[4,4,4,4,4,4]
[7,1,1]=>[[7,7,7],[6,6]]=>[7,7,7]=>[3,3,3,3,3,3,3]
[8,1]=>[[8,8],[7]]=>[8,8]=>[2,2,2,2,2,2,2,2]
[9]=>[[9],[]]=>[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],[]]=>[1,1,1,1,1,1,1,1,1,1]=>[10]
[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]=>[9,1]
[1,1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1]=>[8,1,1]
[1,1,1,1,1,1,4]=>[[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1]=>[7,1,1,1]
[1,1,1,1,1,5]=>[[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1]=>[6,1,1,1,1]
[1,1,1,1,6]=>[[6,1,1,1,1],[]]=>[6,1,1,1,1]=>[5,1,1,1,1,1]
[1,1,1,7]=>[[7,1,1,1],[]]=>[7,1,1,1]=>[4,1,1,1,1,1,1]
[1,1,8]=>[[8,1,1],[]]=>[8,1,1]=>[3,1,1,1,1,1,1,1]
[1,9]=>[[9,1],[]]=>[9,1]=>[2,1,1,1,1,1,1,1,1]
[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]=>[9,9]
[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]=>[8,8,8]
[5,1,1,1,1,1]=>[[5,5,5,5,5,5],[4,4,4,4,4]]=>[5,5,5,5,5,5]=>[6,6,6,6,6]
[6,1,1,1,1]=>[[6,6,6,6,6],[5,5,5,5]]=>[6,6,6,6,6]=>[5,5,5,5,5,5]
[10]=>[[10],[]]=>[10]=>[1,1,1,1,1,1,1,1,1,1]
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.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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