Identifier
Mp00180:
Integer compositions
—to ribbon⟶
Skew partitions
Mp00181: Skew partitions —row lengths⟶ Integer compositions
Mp00181: Skew partitions —row lengths⟶ Integer compositions
Images
=>
Cc0028;cc-rep-1
[1]=>[[1],[]]=>[1]
[1,1]=>[[1,1],[]]=>[1,1]
[2]=>[[2],[]]=>[2]
[1,1,1]=>[[1,1,1],[]]=>[1,1,1]
[1,2]=>[[2,1],[]]=>[2,1]
[2,1]=>[[2,2],[1]]=>[1,2]
[3]=>[[3],[]]=>[3]
[1,1,1,1]=>[[1,1,1,1],[]]=>[1,1,1,1]
[1,1,2]=>[[2,1,1],[]]=>[2,1,1]
[1,2,1]=>[[2,2,1],[1]]=>[1,2,1]
[1,3]=>[[3,1],[]]=>[3,1]
[2,1,1]=>[[2,2,2],[1,1]]=>[1,1,2]
[2,2]=>[[3,2],[1]]=>[2,2]
[3,1]=>[[3,3],[2]]=>[1,3]
[4]=>[[4],[]]=>[4]
[1,1,1,1,1]=>[[1,1,1,1,1],[]]=>[1,1,1,1,1]
[1,1,1,2]=>[[2,1,1,1],[]]=>[2,1,1,1]
[1,1,2,1]=>[[2,2,1,1],[1]]=>[1,2,1,1]
[1,1,3]=>[[3,1,1],[]]=>[3,1,1]
[1,2,1,1]=>[[2,2,2,1],[1,1]]=>[1,1,2,1]
[1,2,2]=>[[3,2,1],[1]]=>[2,2,1]
[1,3,1]=>[[3,3,1],[2]]=>[1,3,1]
[1,4]=>[[4,1],[]]=>[4,1]
[2,1,1,1]=>[[2,2,2,2],[1,1,1]]=>[1,1,1,2]
[2,1,2]=>[[3,2,2],[1,1]]=>[2,1,2]
[2,2,1]=>[[3,3,2],[2,1]]=>[1,2,2]
[2,3]=>[[4,2],[1]]=>[3,2]
[3,1,1]=>[[3,3,3],[2,2]]=>[1,1,3]
[3,2]=>[[4,3],[2]]=>[2,3]
[4,1]=>[[4,4],[3]]=>[1,4]
[5]=>[[5],[]]=>[5]
[1,1,1,1,1,1]=>[[1,1,1,1,1,1],[]]=>[1,1,1,1,1,1]
[1,1,1,1,2]=>[[2,1,1,1,1],[]]=>[2,1,1,1,1]
[1,1,1,2,1]=>[[2,2,1,1,1],[1]]=>[1,2,1,1,1]
[1,1,1,3]=>[[3,1,1,1],[]]=>[3,1,1,1]
[1,1,2,1,1]=>[[2,2,2,1,1],[1,1]]=>[1,1,2,1,1]
[1,1,2,2]=>[[3,2,1,1],[1]]=>[2,2,1,1]
[1,1,3,1]=>[[3,3,1,1],[2]]=>[1,3,1,1]
[1,1,4]=>[[4,1,1],[]]=>[4,1,1]
[1,2,1,1,1]=>[[2,2,2,2,1],[1,1,1]]=>[1,1,1,2,1]
[1,2,1,2]=>[[3,2,2,1],[1,1]]=>[2,1,2,1]
[1,2,2,1]=>[[3,3,2,1],[2,1]]=>[1,2,2,1]
[1,2,3]=>[[4,2,1],[1]]=>[3,2,1]
[1,3,1,1]=>[[3,3,3,1],[2,2]]=>[1,1,3,1]
[1,3,2]=>[[4,3,1],[2]]=>[2,3,1]
[1,4,1]=>[[4,4,1],[3]]=>[1,4,1]
[1,5]=>[[5,1],[]]=>[5,1]
[2,1,1,1,1]=>[[2,2,2,2,2],[1,1,1,1]]=>[1,1,1,1,2]
[2,1,1,2]=>[[3,2,2,2],[1,1,1]]=>[2,1,1,2]
[2,1,2,1]=>[[3,3,2,2],[2,1,1]]=>[1,2,1,2]
[2,1,3]=>[[4,2,2],[1,1]]=>[3,1,2]
[2,2,1,1]=>[[3,3,3,2],[2,2,1]]=>[1,1,2,2]
[2,2,2]=>[[4,3,2],[2,1]]=>[2,2,2]
[2,3,1]=>[[4,4,2],[3,1]]=>[1,3,2]
[2,4]=>[[5,2],[1]]=>[4,2]
[3,1,1,1]=>[[3,3,3,3],[2,2,2]]=>[1,1,1,3]
[3,1,2]=>[[4,3,3],[2,2]]=>[2,1,3]
[3,2,1]=>[[4,4,3],[3,2]]=>[1,2,3]
[3,3]=>[[5,3],[2]]=>[3,3]
[4,1,1]=>[[4,4,4],[3,3]]=>[1,1,4]
[4,2]=>[[5,4],[3]]=>[2,4]
[5,1]=>[[5,5],[4]]=>[1,5]
[6]=>[[6],[]]=>[6]
[1,1,1,1,1,1,1]=>[[1,1,1,1,1,1,1],[]]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,2]=>[[2,1,1,1,1,1],[]]=>[2,1,1,1,1,1]
[1,1,1,1,2,1]=>[[2,2,1,1,1,1],[1]]=>[1,2,1,1,1,1]
[1,1,1,1,3]=>[[3,1,1,1,1],[]]=>[3,1,1,1,1]
[1,1,1,2,1,1]=>[[2,2,2,1,1,1],[1,1]]=>[1,1,2,1,1,1]
[1,1,1,2,2]=>[[3,2,1,1,1],[1]]=>[2,2,1,1,1]
[1,1,1,3,1]=>[[3,3,1,1,1],[2]]=>[1,3,1,1,1]
[1,1,1,4]=>[[4,1,1,1],[]]=>[4,1,1,1]
[1,1,2,1,1,1]=>[[2,2,2,2,1,1],[1,1,1]]=>[1,1,1,2,1,1]
[1,1,2,1,2]=>[[3,2,2,1,1],[1,1]]=>[2,1,2,1,1]
[1,1,2,2,1]=>[[3,3,2,1,1],[2,1]]=>[1,2,2,1,1]
[1,1,2,3]=>[[4,2,1,1],[1]]=>[3,2,1,1]
[1,1,3,1,1]=>[[3,3,3,1,1],[2,2]]=>[1,1,3,1,1]
[1,1,3,2]=>[[4,3,1,1],[2]]=>[2,3,1,1]
[1,1,4,1]=>[[4,4,1,1],[3]]=>[1,4,1,1]
[1,1,5]=>[[5,1,1],[]]=>[5,1,1]
[1,2,1,1,1,1]=>[[2,2,2,2,2,1],[1,1,1,1]]=>[1,1,1,1,2,1]
[1,2,1,1,2]=>[[3,2,2,2,1],[1,1,1]]=>[2,1,1,2,1]
[1,2,1,2,1]=>[[3,3,2,2,1],[2,1,1]]=>[1,2,1,2,1]
[1,2,1,3]=>[[4,2,2,1],[1,1]]=>[3,1,2,1]
[1,2,2,1,1]=>[[3,3,3,2,1],[2,2,1]]=>[1,1,2,2,1]
[1,2,2,2]=>[[4,3,2,1],[2,1]]=>[2,2,2,1]
[1,2,3,1]=>[[4,4,2,1],[3,1]]=>[1,3,2,1]
[1,2,4]=>[[5,2,1],[1]]=>[4,2,1]
[1,3,1,1,1]=>[[3,3,3,3,1],[2,2,2]]=>[1,1,1,3,1]
[1,3,1,2]=>[[4,3,3,1],[2,2]]=>[2,1,3,1]
[1,3,2,1]=>[[4,4,3,1],[3,2]]=>[1,2,3,1]
[1,3,3]=>[[5,3,1],[2]]=>[3,3,1]
[1,4,1,1]=>[[4,4,4,1],[3,3]]=>[1,1,4,1]
[1,4,2]=>[[5,4,1],[3]]=>[2,4,1]
[1,5,1]=>[[5,5,1],[4]]=>[1,5,1]
[1,6]=>[[6,1],[]]=>[6,1]
[2,1,1,1,1,1]=>[[2,2,2,2,2,2],[1,1,1,1,1]]=>[1,1,1,1,1,2]
[2,1,1,1,2]=>[[3,2,2,2,2],[1,1,1,1]]=>[2,1,1,1,2]
[2,1,1,2,1]=>[[3,3,2,2,2],[2,1,1,1]]=>[1,2,1,1,2]
[2,1,1,3]=>[[4,2,2,2],[1,1,1]]=>[3,1,1,2]
[2,1,2,1,1]=>[[3,3,3,2,2],[2,2,1,1]]=>[1,1,2,1,2]
[2,1,2,2]=>[[4,3,2,2],[2,1,1]]=>[2,2,1,2]
[2,1,3,1]=>[[4,4,2,2],[3,1,1]]=>[1,3,1,2]
[2,1,4]=>[[5,2,2],[1,1]]=>[4,1,2]
[2,2,1,1,1]=>[[3,3,3,3,2],[2,2,2,1]]=>[1,1,1,2,2]
[2,2,1,2]=>[[4,3,3,2],[2,2,1]]=>[2,1,2,2]
[2,2,2,1]=>[[4,4,3,2],[3,2,1]]=>[1,2,2,2]
[2,2,3]=>[[5,3,2],[2,1]]=>[3,2,2]
[2,3,1,1]=>[[4,4,4,2],[3,3,1]]=>[1,1,3,2]
[2,3,2]=>[[5,4,2],[3,1]]=>[2,3,2]
[2,4,1]=>[[5,5,2],[4,1]]=>[1,4,2]
[2,5]=>[[6,2],[1]]=>[5,2]
[3,1,1,1,1]=>[[3,3,3,3,3],[2,2,2,2]]=>[1,1,1,1,3]
[3,1,1,2]=>[[4,3,3,3],[2,2,2]]=>[2,1,1,3]
[3,1,2,1]=>[[4,4,3,3],[3,2,2]]=>[1,2,1,3]
[3,1,3]=>[[5,3,3],[2,2]]=>[3,1,3]
[3,2,1,1]=>[[4,4,4,3],[3,3,2]]=>[1,1,2,3]
[3,2,2]=>[[5,4,3],[3,2]]=>[2,2,3]
[3,3,1]=>[[5,5,3],[4,2]]=>[1,3,3]
[3,4]=>[[6,3],[2]]=>[4,3]
[4,1,1,1]=>[[4,4,4,4],[3,3,3]]=>[1,1,1,4]
[4,1,2]=>[[5,4,4],[3,3]]=>[2,1,4]
[4,2,1]=>[[5,5,4],[4,3]]=>[1,2,4]
[4,3]=>[[6,4],[3]]=>[3,4]
[5,1,1]=>[[5,5,5],[4,4]]=>[1,1,5]
[5,2]=>[[6,5],[4]]=>[2,5]
[6,1]=>[[6,6],[5]]=>[1,6]
[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]
[1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,3]=>[[3,1,1,1,1,1],[]]=>[3,1,1,1,1,1]
[1,1,1,1,4]=>[[4,1,1,1,1],[]]=>[4,1,1,1,1]
[1,1,1,5]=>[[5,1,1,1],[]]=>[5,1,1,1]
[1,1,6]=>[[6,1,1],[]]=>[6,1,1]
[1,7]=>[[7,1],[]]=>[7,1]
[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]
[1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1]
[1,1,1,1,1,4]=>[[4,1,1,1,1,1],[]]=>[4,1,1,1,1,1]
[1,1,1,1,5]=>[[5,1,1,1,1],[]]=>[5,1,1,1,1]
[1,1,1,6]=>[[6,1,1,1],[]]=>[6,1,1,1]
[1,1,7]=>[[7,1,1],[]]=>[7,1,1]
[1,8]=>[[8,1],[]]=>[8,1]
[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]
[1,1,1,1,1,1,1,1,2]=>[[2,1,1,1,1,1,1,1,1],[]]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,3]=>[[3,1,1,1,1,1,1,1],[]]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,4]=>[[4,1,1,1,1,1,1],[]]=>[4,1,1,1,1,1,1]
[1,1,1,1,1,5]=>[[5,1,1,1,1,1],[]]=>[5,1,1,1,1,1]
[1,1,1,1,6]=>[[6,1,1,1,1],[]]=>[6,1,1,1,1]
[1,1,1,7]=>[[7,1,1,1],[]]=>[7,1,1,1]
[1,1,8]=>[[8,1,1],[]]=>[8,1,1]
[1,9]=>[[9,1],[]]=>[9,1]
[10]=>[[10],[]]=>[10]
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
row lengths
Description
The sequence of row lengths from top to bottom.
searching the database
Sorry, this map was not found in the database.