Identifier
Mp00052: Parking functions —to non-decreasing parking function⟶ Parking functions
Mp00319: Parking functions —to composition⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Images
[1] => [1] => [1] => [1]
[1,1] => [1,1] => [1,1] => [1,1]
[1,2] => [1,2] => [1,2] => [1,2]
[2,1] => [1,2] => [1,2] => [1,2]
[1,1,1] => [1,1,1] => [1,1,1] => [1,1,1]
[1,1,2] => [1,1,2] => [1,1,2] => [1,1,2]
[1,2,1] => [1,1,2] => [1,1,2] => [1,1,2]
[2,1,1] => [1,1,2] => [1,1,2] => [1,1,2]
[1,1,3] => [1,1,3] => [1,1,3] => [1,1,3]
[1,3,1] => [1,1,3] => [1,1,3] => [1,1,3]
[3,1,1] => [1,1,3] => [1,1,3] => [1,1,3]
[1,2,2] => [1,2,2] => [1,2,2] => [1,2,2]
[2,1,2] => [1,2,2] => [1,2,2] => [1,2,2]
[2,2,1] => [1,2,2] => [1,2,2] => [1,2,2]
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3]
[1,3,2] => [1,2,3] => [1,2,3] => [1,2,3]
[2,1,3] => [1,2,3] => [1,2,3] => [1,2,3]
[2,3,1] => [1,2,3] => [1,2,3] => [1,2,3]
[3,1,2] => [1,2,3] => [1,2,3] => [1,2,3]
[3,2,1] => [1,2,3] => [1,2,3] => [1,2,3]
[1,1,1,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1,1]
[1,1,1,2] => [1,1,1,2] => [1,1,1,2] => [1,1,1,2]
[1,1,2,1] => [1,1,1,2] => [1,1,1,2] => [1,1,1,2]
[1,2,1,1] => [1,1,1,2] => [1,1,1,2] => [1,1,1,2]
[2,1,1,1] => [1,1,1,2] => [1,1,1,2] => [1,1,1,2]
[1,1,1,3] => [1,1,1,3] => [1,1,1,3] => [1,1,1,3]
[1,1,3,1] => [1,1,1,3] => [1,1,1,3] => [1,1,1,3]
[1,3,1,1] => [1,1,1,3] => [1,1,1,3] => [1,1,1,3]
[3,1,1,1] => [1,1,1,3] => [1,1,1,3] => [1,1,1,3]
[1,1,1,4] => [1,1,1,4] => [1,1,1,4] => [1,1,1,4]
[1,1,4,1] => [1,1,1,4] => [1,1,1,4] => [1,1,1,4]
[1,4,1,1] => [1,1,1,4] => [1,1,1,4] => [1,1,1,4]
[4,1,1,1] => [1,1,1,4] => [1,1,1,4] => [1,1,1,4]
[1,1,2,2] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[1,2,1,2] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[1,2,2,1] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[2,1,1,2] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[2,1,2,1] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[2,2,1,1] => [1,1,2,2] => [1,1,2,2] => [1,1,2,2]
[1,1,2,3] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,1,3,2] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,2,1,3] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,2,3,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,3,1,2] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,3,2,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[2,1,1,3] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[2,1,3,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[2,3,1,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[3,1,1,2] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[3,1,2,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[3,2,1,1] => [1,1,2,3] => [1,1,2,3] => [1,1,2,3]
[1,1,2,4] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,1,4,2] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,2,1,4] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,2,4,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,4,1,2] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,4,2,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[2,1,1,4] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[2,1,4,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[2,4,1,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[4,1,1,2] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[4,1,2,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[4,2,1,1] => [1,1,2,4] => [1,1,2,4] => [1,1,2,4]
[1,1,3,3] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[1,3,1,3] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[1,3,3,1] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[3,1,1,3] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[3,1,3,1] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[3,3,1,1] => [1,1,3,3] => [1,1,3,3] => [1,1,3,3]
[1,1,3,4] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,1,4,3] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,3,1,4] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,3,4,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,4,1,3] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,4,3,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[3,1,1,4] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[3,1,4,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[3,4,1,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[4,1,1,3] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[4,1,3,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[4,3,1,1] => [1,1,3,4] => [1,1,3,4] => [1,1,3,4]
[1,2,2,2] => [1,2,2,2] => [1,2,2,2] => [1,2,2,2]
[2,1,2,2] => [1,2,2,2] => [1,2,2,2] => [1,2,2,2]
[2,2,1,2] => [1,2,2,2] => [1,2,2,2] => [1,2,2,2]
[2,2,2,1] => [1,2,2,2] => [1,2,2,2] => [1,2,2,2]
[1,2,2,3] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[1,2,3,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[1,3,2,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,1,2,3] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,1,3,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,2,1,3] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,2,3,1] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,3,1,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[2,3,2,1] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[3,1,2,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[3,2,1,2] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[3,2,2,1] => [1,2,2,3] => [1,2,2,3] => [1,2,2,3]
[1,2,2,4] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[1,2,4,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[1,4,2,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[2,1,2,4] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
>>> Load all 601 entries. <<<
[2,1,4,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[2,2,1,4] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[2,2,4,1] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[2,4,1,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[2,4,2,1] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[4,1,2,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[4,2,1,2] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[4,2,2,1] => [1,2,2,4] => [1,2,2,4] => [1,2,2,4]
[1,2,3,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[1,3,2,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[1,3,3,2] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[2,1,3,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[2,3,1,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[2,3,3,1] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,1,2,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,1,3,2] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,2,1,3] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,2,3,1] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,3,1,2] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[3,3,2,1] => [1,2,3,3] => [1,2,3,3] => [1,2,3,3]
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,2,4,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,3,2,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,3,4,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,4,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,4,3,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,1,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,1,4,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,3,1,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,4,1,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[2,4,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,1,2,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,1,4,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,2,1,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,2,4,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,1,3,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,2,1,3] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[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] => [1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2]
[1,1,1,2,1] => [1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2]
[1,1,2,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2]
[1,2,1,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2]
[2,1,1,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2]
[1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3]
[1,1,1,3,1] => [1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3]
[1,1,3,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3]
[1,3,1,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3]
[3,1,1,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3]
[1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4]
[1,1,1,4,1] => [1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4]
[1,1,4,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4]
[1,4,1,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4]
[4,1,1,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4]
[1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5]
[1,1,1,5,1] => [1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5]
[1,1,5,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5]
[1,5,1,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5]
[5,1,1,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5]
[1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,1,2,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,1,2,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,2,1,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,2,1,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,2,2,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[2,1,1,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[2,1,1,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[2,1,2,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[2,2,1,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2]
[1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,1,3,2] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,2,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,2,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,3,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,3,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,2,1,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,2,1,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,2,3,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,3,1,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,3,1,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,3,2,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[2,1,1,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[2,1,1,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[2,1,3,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[2,3,1,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[3,1,1,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[3,1,1,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[3,1,2,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[3,2,1,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3]
[1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,1,4,2] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,2,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,2,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,4,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,4,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,2,1,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,2,1,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,2,4,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,4,1,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,4,1,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,4,2,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[2,1,1,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[2,1,1,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[2,1,4,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[2,4,1,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[4,1,1,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[4,1,1,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[4,1,2,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[4,2,1,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4]
[1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,1,5,2] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,2,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,2,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,5,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,5,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,2,1,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,2,1,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,2,5,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,5,1,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,5,1,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,5,2,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[2,1,1,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[2,1,1,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[2,1,5,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[2,5,1,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[5,1,1,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[5,1,1,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[5,1,2,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[5,2,1,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5]
[1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,1,3,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,1,3,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,3,1,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,3,1,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,3,3,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[3,1,1,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[3,1,1,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[3,1,3,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[3,3,1,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3]
[1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,1,4,3] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,3,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,3,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,4,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,4,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,3,1,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,3,1,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,3,4,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,4,1,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,4,1,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,4,3,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[3,1,1,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[3,1,1,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[3,1,4,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[3,4,1,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[4,1,1,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[4,1,1,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[4,1,3,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[4,3,1,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4]
[1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[1,2,1,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[1,2,2,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[1,2,2,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,1,1,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,1,2,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,1,2,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,2,1,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,2,1,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[2,2,2,1,1] => [1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2]
[1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,1,2,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,1,3,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,1,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,1,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,2,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,2,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,3,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,2,3,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,3,1,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,3,2,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,3,2,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,1,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,1,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,2,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,2,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,3,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,1,3,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,2,1,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,2,1,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,2,3,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,3,1,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,3,1,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[2,3,2,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,1,1,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,1,2,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,1,2,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,2,1,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,2,1,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[3,2,2,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3]
[1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,1,2,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,1,4,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,1,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,1,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,2,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,2,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,4,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,2,4,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,4,1,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,4,2,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,4,2,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,1,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,1,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,2,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,2,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,4,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,1,4,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,2,1,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,2,1,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,2,4,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,4,1,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,4,1,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[2,4,2,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,1,1,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,1,2,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,1,2,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,2,1,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,2,1,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[4,2,2,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4]
[1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,1,3,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,1,3,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,2,1,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,2,3,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,2,3,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,1,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,1,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,2,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,2,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,3,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,3,3,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,1,1,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,1,3,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,1,3,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,3,1,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,3,1,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[2,3,3,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,1,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,1,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,2,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,2,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,3,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,1,3,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,2,1,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,2,1,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,2,3,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,3,1,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,3,1,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[3,3,2,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3]
[1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2]
[2,1,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2]
[2,2,1,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2]
[2,2,2,1,2] => [1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2]
[2,2,2,2,1] => [1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2]
[1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[1,2,2,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[1,2,3,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[1,3,2,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,1,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,1,2,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,1,3,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,1,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,1,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,2,1,3] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,2,3,1] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,3,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,2,3,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,3,1,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,3,2,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[2,3,2,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[3,1,2,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[3,2,1,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[3,2,2,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[3,2,2,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3]
[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] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[1,1,1,1,2,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[1,1,1,2,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[1,1,2,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[1,2,1,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2]
[1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,1,1,1,3,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,1,1,3,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,1,3,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,3,1,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3]
[1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,1,1,1,4,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,1,1,4,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,1,4,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,4,1,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[4,1,1,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4]
[1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,1,1,1,5,1] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,1,1,5,1,1] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,1,5,1,1,1] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,5,1,1,1,1] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[5,1,1,1,1,1] => [1,1,1,1,1,5] => [1,1,1,1,1,5] => [1,1,1,1,1,5]
[1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,1,2,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,1,2,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,2,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,2,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,2,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,2,1,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,2,1,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,2,1,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,2,2,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[2,1,1,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[2,1,1,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[2,1,1,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[2,1,2,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2]
[1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,1,3,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,2,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,2,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,3,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,3,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,2,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,2,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,2,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,3,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,3,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,3,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,2,1,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,2,1,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,2,1,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,2,3,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,3,1,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,3,1,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,3,1,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,3,2,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[2,1,1,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[2,1,1,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[2,1,1,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[2,1,3,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[2,3,1,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[3,1,1,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[3,1,1,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[3,1,1,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[3,1,2,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[3,2,1,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3]
[1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,1,4,2] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,2,1,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,2,4,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,4,1,2] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,4,2,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,2,1,1,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,2,1,4,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,2,4,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,4,1,1,2] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,4,1,2,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,4,2,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,2,1,1,1,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,2,1,1,4,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,2,1,4,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,2,4,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,4,1,1,1,2] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,4,1,1,2,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,4,1,2,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,4,2,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[2,1,1,1,1,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[2,1,1,1,4,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[2,1,1,4,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[2,1,4,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[2,4,1,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[4,1,1,1,1,2] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[4,1,1,1,2,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[4,1,1,2,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[4,1,2,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[4,2,1,1,1,1] => [1,1,1,1,2,4] => [1,1,1,1,2,4] => [1,1,1,1,2,4]
[1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,1,3,1,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,1,3,3,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,3,1,1,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,3,1,3,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,3,3,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,3,1,1,1,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,3,1,1,3,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,3,1,3,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,3,3,1,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[3,1,1,1,1,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[3,1,1,1,3,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[3,1,1,3,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[3,1,3,1,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[3,3,1,1,1,1] => [1,1,1,1,3,3] => [1,1,1,1,3,3] => [1,1,1,1,3,3]
[1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,1,2,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,1,2,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,1,2,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,1,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,1,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,1,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,2,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,2,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,2,2,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,1,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,1,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,1,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,2,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,2,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,1,2,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,2,1,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,2,1,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,2,1,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[2,2,2,1,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2]
[1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,1,2,3,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,1,3,2,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,1,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,1,3,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,2,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,2,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,3,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,3,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,3,1,2,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,3,2,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,3,2,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,1,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,1,3,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,2,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,2,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,3,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,1,3,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,2,1,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,2,1,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,2,3,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,3,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,3,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,2,3,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,1,1,2,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,1,2,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,1,2,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,2,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,2,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,3,2,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,1,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,1,3,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,2,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,2,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,3,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,1,3,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,2,1,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,2,1,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,2,3,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,3,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,3,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,1,3,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,2,1,1,1,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,2,1,1,3,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,2,1,3,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,2,3,1,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,3,1,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,3,1,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,3,1,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[2,3,2,1,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,1,1,2,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,1,2,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,1,2,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,2,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,2,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,1,2,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,2,1,1,1,2] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,2,1,1,2,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,2,1,2,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[3,2,2,1,1,1] => [1,1,1,2,2,3] => [1,1,1,2,2,3] => [1,1,1,2,2,3]
[1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[1,2,1,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[1,2,2,1,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[1,2,2,2,1,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[1,2,2,2,2,1] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,1,1,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,1,2,1,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,1,2,2,1,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,1,2,2,2,1] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,1,1,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,1,2,1,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,1,2,2,1] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,2,1,1,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,2,1,2,1] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
[2,2,2,2,1,1] => [1,1,2,2,2,2] => [1,1,2,2,2,2] => [1,1,2,2,2,2]
Map
to non-decreasing parking function
Description
Return the non-decreasing parking function which underlies the parking function.
Sorts the parking function into an increasing sequence.
Map
to composition
Description
Return the parking function interpreted as an integer composition.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00314Foata bijection.