Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0005;cc-rep-1Cc0002;cc-rep-3
[1]=>[1,0]=>[2,1]=>[2] [1,1]=>[1,0,1,0]=>[3,1,2]=>[3] [2]=>[1,1,0,0]=>[2,3,1]=>[3] [1,1,1]=>[1,0,1,0,1,0]=>[4,1,2,3]=>[4] [1,2]=>[1,0,1,1,0,0]=>[3,1,4,2]=>[4] [2,1]=>[1,1,0,0,1,0]=>[2,4,1,3]=>[4] [3]=>[1,1,1,0,0,0]=>[2,3,4,1]=>[4] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>[5] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>[5] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>[5] [1,3]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>[5] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>[5] [2,2]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>[5] [3,1]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>[5] [4]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>[6] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>[6] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>[6] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>[6] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[6] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>[6] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>[6] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>[6] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>[6] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[6] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>[6] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>[6] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>[6] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>[6] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>[6] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6] [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]=>[7] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>[7] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>[7] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>[7] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>[7] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>[7] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[7] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>[7] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[7] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>[7] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>[7] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>[7] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>[7] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>[7] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[7] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>[7] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>[7] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[7] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>[7] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>[7] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>[7] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>[7] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>[7] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>[7] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>[7] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>[7] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>[7] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>[7] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>[7] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>[7] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>[7] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [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]=>[8] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8]
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
cycle type
Description
The cycle type of a permutation as a partition.