- FindStat

Identifier

Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions

Images

[1] => [1,0] => [2,1] => {{1,2}}

[1,1] => [1,0,1,0] => [3,1,2] => {{1,2,3}}

[2] => [1,1,0,0] => [2,3,1] => {{1,2,3}}

[1,1,1] => [1,0,1,0,1,0] => [4,1,2,3] => {{1,2,3,4}}

[1,2] => [1,0,1,1,0,0] => [3,1,4,2] => {{1,2,3,4}}

[2,1] => [1,1,0,0,1,0] => [2,4,1,3] => {{1,2,3,4}}

[3] => [1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}}

[1,1,1,1] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => {{1,2,3,4,5}}

[1,1,2] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => {{1,2,3,4,5}}

[1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => {{1,2,3,4,5}}

[1,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => {{1,2,3,4,5}}

[2,1,1] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => {{1,2,3,4,5}}

[2,2] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => {{1,2,3,4,5}}

[3,1] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => {{1,2,3,4,5}}

[4] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}}

[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => {{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] => {{1,2,3,4,5,6}}

[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}}

[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}}

[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}}

[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}}

[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}}

[1,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}}

[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}}

[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}}

[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}}

[2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}}

[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}}

[3,2] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}}

[4,1] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}}

[5] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}}

[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] => {{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] => {{1,2,3,4,5,6,7}}

[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => {{1,2,3,4,5,6,7}}

[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => {{1,2,3,4,5,6,7}}

[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => {{1,2,3,4,5,6,7}}

[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => {{1,2,3,4,5,6,7}}

[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => {{1,2,3,4,5,6,7}}

[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => {{1,2,3,4,5,6,7}}

[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => {{1,2,3,4,5,6,7}}

[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => {{1,2,3,4,5,6,7}}

[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7}}

[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => {{1,2,3,4,5,6,7}}

[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => {{1,2,3,4,5,6,7}}

[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => {{1,2,3,4,5,6,7}}

[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => {{1,2,3,4,5,6,7}}

[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => {{1,2,3,4,5,6,7}}

[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => {{1,2,3,4,5,6,7}}

[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,3,4,5,6,7}}

[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => {{1,2,3,4,5,6,7}}

[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => {{1,2,3,4,5,6,7}}

[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => {{1,2,3,4,5,6,7}}

[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,3,4,5,6,7}}

[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => {{1,2,3,4,5,6,7}}

[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => {{1,2,3,4,5,6,7}}

[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => {{1,2,3,4,5,6,7}}

[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,4,5,6,7}}

[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => {{1,2,3,4,5,6,7}}

[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,4,5,6,7}}

[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,5,6,7}}

[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,5,6,7}}

[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,6,7}}

[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => {{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] => {{1,2,3,4,5,6,7,8}}

[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [4,1,2,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,4,7,2,5,8,6] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,4,6,2,7,8,5] => {{1,2,3,4,5,6,7,8}}

[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [3,1,4,5,8,2,6,7] => {{1,2,3,4,5,6,7,8}}

[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,1,4,5,7,2,8,6] => {{1,2,3,4,5,6,7,8}}

[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,8,2,7] => {{1,2,3,4,5,6,7,8}}

[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,7,1,3,4,5,8,6] => {{1,2,3,4,5,6,7,8}}

[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,6,1,3,4,8,5,7] => {{1,2,3,4,5,6,7,8}}

[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,6,1,3,4,7,8,5] => {{1,2,3,4,5,6,7,8}}

[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,5,1,3,8,4,6,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

>>> Load all 235 entries. <<<

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,4,1,5,8,3,6,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1,5,6,8,3,7] => {{1,2,3,4,5,6,7,8}}

[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,4,1,5,6,7,8,3] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,3,6,1,4,8,5,7] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,3,5,1,8,4,6,7] => {{1,2,3,4,5,6,7,8}}

[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,3,5,1,7,4,8,6] => {{1,2,3,4,5,6,7,8}}

[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,5,1,6,8,4,7] => {{1,2,3,4,5,6,7,8}}

[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,5,1,6,7,8,4] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,3,4,6,1,7,8,5] => {{1,2,3,4,5,6,7,8}}

[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] => {{1,2,3,4,5,6,7,8}}

[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,6,7,8}}

[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,7,8}}

[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}}

[1,1,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,2] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,1,2,3,4,5,8,9,6] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [6,1,2,3,4,9,5,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,1,2,3,4,8,5,9,7] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [6,1,2,3,4,7,9,5,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,1,2,3,4,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [5,1,2,3,9,4,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [5,1,2,3,8,4,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [4,1,2,8,3,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,2,5,9,3,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,9,3,8] => {{1,2,3,4,5,6,7,8,9}}

[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}}

[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,9,2,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,8,2,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[1,2,2,2,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,4,9,2,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,4,5,6,9,2,7,8] => {{1,2,3,4,5,6,7,8,9}}

[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,8,2,9,7] => {{1,2,3,4,5,6,7,8,9}}

[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,9,2,8] => {{1,2,3,4,5,6,7,8,9}}

[1,7] => [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] => {{1,2,3,4,5,6,7,8,9}}

[2,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,8,1,3,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,7,1,3,4,5,9,6,8] => {{1,2,3,4,5,6,7,8,9}}

[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,7,1,3,4,5,8,9,6] => {{1,2,3,4,5,6,7,8,9}}

[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,6,1,3,4,9,5,7,8] => {{1,2,3,4,5,6,7,8,9}}

[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,5,1,3,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,8,5,9,7] => {{1,2,3,4,5,6,7,8,9}}

[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,4,1,5,9,3,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1,5,6,7,9,3,8] => {{1,2,3,4,5,6,7,8,9}}

[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,3] => {{1,2,3,4,5,6,7,8,9}}

[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,9,1,4,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,8,1,4,5,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [2,3,5,1,6,7,9,4,8] => {{1,2,3,4,5,6,7,8,9}}

[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,5,1,6,7,8,9,4] => {{1,2,3,4,5,6,7,8,9}}

[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,9,1,5,6,7,8] => {{1,2,3,4,5,6,7,8,9}}

[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,6,1,7,8,9,5] => {{1,2,3,4,5,6,7,8,9}}

[5,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [2,3,4,5,8,1,6,9,7] => {{1,2,3,4,5,6,7,8,9}}

[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,7,1,8,9,6] => {{1,2,3,4,5,6,7,8,9}}

[6,1,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,8,1,9,7] => {{1,2,3,4,5,6,7,8,9}}

[7,1] => [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] => {{1,2,3,4,5,6,7,8,9}}

[8] => [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] => {{1,2,3,4,5,6,7,8,9}}

[1,1,1,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,2] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,1,2,3,4,5,6,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,1,2,3,4,5,9,6,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,1,2,3,4,5,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,1,2,3,4,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [5,1,2,3,10,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,1,2,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,2,10,3,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,1,2,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,9,2,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,10,4,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,2,2,2,2] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,10,2,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [3,1,4,5,6,7,9,2,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,10,2,9] => {{1,2,3,4,5,6,7,8,9,10}}

[1,8] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[2,1,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,9,1,3,4,5,6,7,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,8,1,3,4,5,6,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,5,1,3,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,10,7,9] => {{1,2,3,4,5,6,7,8,9,10}}

[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,4,1,5,6,7,8,10,3,9] => {{1,2,3,4,5,6,7,8,9,10}}

[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,3] => {{1,2,3,4,5,6,7,8,9,10}}

[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,10,1,4,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,4] => {{1,2,3,4,5,6,7,8,9,10}}

[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,10,1,5,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,5] => {{1,2,3,4,5,6,7,8,9,10}}

[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,10,1,6,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,7,1,8,9,10,6] => {{1,2,3,4,5,6,7,8,9,10}}

[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,10,1,7,8,9] => {{1,2,3,4,5,6,7,8,9,10}}

[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,8,1,9,10,7] => {{1,2,3,4,5,6,7,8,9,10}}

[7,1,1] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,9,1,10,8] => {{1,2,3,4,5,6,7,8,9,10}}

[8,1] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[9] => [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] => {{1,2,3,4,5,6,7,8,9,10}}

[1,1,1,1,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,1,1,1,2] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,1,2,3,4,5,11,6,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,11,2,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,2] => {{1,2,3,4,5,6,7,8,9,10,11}}

[2,1,1,1,1,1,1,1,1] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,10,1,3,4,5,6,7,8,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,1,5,6,7,8,9,10,11,3] => {{1,2,3,4,5,6,7,8,9,10,11}}

[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,11,1,4,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,5,1,6,7,8,9,10,11,4] => {{1,2,3,4,5,6,7,8,9,10,11}}

[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,11,1,5,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,1,7,8,9,10,11,5] => {{1,2,3,4,5,6,7,8,9,10,11}}

[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,11,1,6,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,7,1,8,9,10,11,6] => {{1,2,3,4,5,6,7,8,9,10,11}}

[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,11,1,7,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,6,8,1,9,10,11,7] => {{1,2,3,4,5,6,7,8,9,10,11}}

[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,11,1,8,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [2,3,4,5,6,7,9,1,10,11,8] => {{1,2,3,4,5,6,7,8,9,10,11}}

[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [2,3,4,5,6,7,8,11,1,9,10] => {{1,2,3,4,5,6,7,8,9,10,11}}

[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [2,3,4,5,6,7,8,10,1,11,9] => {{1,2,3,4,5,6,7,8,9,10,11}}

[9,1] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[10] => [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] => {{1,2,3,4,5,6,7,8,9,10,11}}

[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,11,12,2] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [2,3,4,5,6,7,8,9,10,12,1,11] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,1,1,1,1,1,1,1,1,2] => [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] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

[1,2,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,9,6,11,8,12,10] => {{1,2,3,4,5,6,7,8,9,10,11,12}}

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

to cycle type

Description

Let

$\pi=c_1\dots c_r$ a permutation of size

$n$ decomposed in its cyclic parts. The associated set partition of

$[n]$ then is

$S=S_1\cup\dots\cup S_r$ such that

$S_i$ is the set of integers in the cycle

$c_i$ .
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].