Identifier
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Images
[1] => [1,0] => [1] => [1]
[2] => [1,0,1,0] => [2,1] => [2,1]
[1,1] => [1,1,0,0] => [1,2] => [1,2]
[3] => [1,0,1,0,1,0] => [3,2,1] => [3,2,1]
[2,1] => [1,0,1,1,0,0] => [2,3,1] => [2,3,1]
[1,1,1] => [1,1,0,1,0,0] => [2,1,3] => [2,1,3]
[4] => [1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1]
[3,1] => [1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,4,2,1]
[2,2] => [1,1,1,0,0,0] => [1,2,3] => [1,2,3]
[2,1,1] => [1,0,1,1,0,1,0,0] => [3,2,4,1] => [3,2,4,1]
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4]
[5] => [1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1]
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [4,5,3,2,1]
[3,2] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1]
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [4,3,5,2,1]
[2,2,1] => [1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,3,2,4]
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1]
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5]
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1]
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,4,5,2,1]
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1]
[3,3] => [1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4]
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [2,4,3,5,1]
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1]
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4]
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [1,4,3,2,5]
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1]
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6]
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1]
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [6,7,5,4,3,2,1]
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [4,5,6,3,2,1]
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [6,5,7,4,3,2,1]
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,2,4,5,1]
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [3,5,4,6,2,1]
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [6,5,4,7,3,2,1]
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [2,1,4,3,5]
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,3,4,5,1]
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [2,5,4,3,6,1]
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [6,5,4,3,7,2,1]
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [1,2,4,3,5]
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [1,5,4,3,2,6]
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [6,5,4,3,2,7,1]
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7]
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1]
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [7,8,6,5,4,3,2,1]
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1]
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [7,6,8,5,4,3,2,1]
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,6,2,1]
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [4,6,5,7,3,2,1]
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [7,6,5,8,4,3,2,1]
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5]
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [3,2,5,4,6,1]
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [3,4,5,6,2,1]
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [3,6,5,4,7,2,1]
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [7,6,5,4,8,3,2,1]
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,3,1,4,5]
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [2,1,5,4,3,6]
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [2,3,5,4,6,1]
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [2,6,5,4,3,7,1]
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,8,2,1]
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5]
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [1,2,5,4,3,6]
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [1,6,5,4,3,2,7]
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,8,1]
[1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1,8]
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1]
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [8,9,7,6,5,4,3,2,1]
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [6,7,8,5,4,3,2,1]
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [8,7,9,6,5,4,3,2,1]
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1]
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [5,7,6,8,4,3,2,1]
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [8,7,6,9,5,4,3,2,1]
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1]
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [4,3,6,5,7,2,1]
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1]
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [4,7,6,5,8,3,2,1]
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [8,7,6,5,9,4,3,2,1]
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [3,2,1,5,4,6]
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,4,2,5,6,1]
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [3,2,6,5,4,7,1]
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [3,4,6,5,7,2,1]
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [3,7,6,5,4,8,2,1]
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [8,7,6,5,4,9,3,2,1]
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5]
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [2,3,1,5,4,6]
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [2,1,6,5,4,3,7]
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1]
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [2,3,6,5,4,7,1]
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [2,7,6,5,4,3,8,1]
[3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [8,7,6,5,4,3,9,2,1]
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [2,1,3,5,4,6]
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [1,2,6,5,4,3,7]
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [1,7,6,5,4,3,2,8]
[2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [8,7,6,5,4,3,2,9,1]
[1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9]
[10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [10,9,8,7,6,5,4,3,2,1]
[9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [9,10,8,7,6,5,4,3,2,1]
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [7,8,9,6,5,4,3,2,1]
[8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [9,8,10,7,6,5,4,3,2,1]
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [6,5,7,8,4,3,2,1]
>>> Load all 375 entries. <<<
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [6,8,7,9,5,4,3,2,1]
[7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [9,8,7,10,6,5,4,3,2,1]
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1]
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [5,4,7,6,8,3,2,1]
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [5,6,7,8,4,3,2,1]
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [8,7,5,6,9,4,3,2,1] => [5,8,7,6,9,4,3,2,1]
[6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [9,8,7,6,10,5,4,3,2,1]
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6]
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [4,3,2,6,5,7,1]
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1]
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [4,3,7,6,5,8,2,1]
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [4,5,7,6,8,3,2,1]
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,5,9,3,2,1] => [4,8,7,6,5,9,3,2,1]
[5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [9,8,7,6,5,10,4,3,2,1]
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,4,2,1,5,6]
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [3,2,1,6,5,4,7]
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1]
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [3,4,2,6,5,7,1]
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [3,2,7,6,5,4,8,1]
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1]
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [3,4,7,6,5,8,2,1]
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,4,9,2,1] => [3,8,7,6,5,4,9,2,1]
[4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [9,8,7,6,5,4,10,3,2,1]
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [1,2,3,5,4,6]
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6]
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [2,3,1,6,5,4,7]
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [2,1,7,6,5,4,3,8]
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [3,2,4,6,5,7,1]
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [2,3,7,6,5,4,8,1]
[3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [2,8,7,6,5,4,3,9,1]
[3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [9,8,7,6,5,4,3,10,2,1]
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6]
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [2,1,3,6,5,4,7]
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [1,2,7,6,5,4,3,8]
[2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [1,8,7,6,5,4,3,2,9]
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [9,8,7,6,5,4,3,2,10,1]
[1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [9,8,7,6,5,4,3,2,1,10]
[11] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [11,10,9,8,7,6,5,4,3,2,1]
[10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [10,11,9,8,7,6,5,4,3,2,1]
[9,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [8,9,10,7,6,5,4,3,2,1]
[9,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [10,9,11,8,7,6,5,4,3,2,1]
[8,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [7,6,8,9,5,4,3,2,1] => [7,6,8,9,5,4,3,2,1]
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [6,5,4,7,8,3,2,1]
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [6,7,8,9,5,4,3,2,1]
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1]
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [5,4,3,7,6,8,2,1]
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [5,6,4,7,8,3,2,1]
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [4,3,2,1,6,5,7]
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1]
[5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,8,1] => [4,3,2,7,6,5,8,1]
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1]
[5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,2,1] => [4,5,3,7,6,8,2,1]
[5,3,1,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,5,9,2,1] => [4,3,8,7,6,5,9,2,1]
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [5,4,6,7,8,3,2,1]
[5,2,2,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,6,9,3,2,1] => [4,5,8,7,6,9,3,2,1]
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6]
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [3,4,2,1,6,5,7]
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [3,2,1,7,6,5,4,8]
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [2,3,4,6,5,7,1]
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1]
[4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,5,8,1] => [3,4,2,7,6,5,8,1]
[4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,6,8,2,1] => [4,3,5,7,6,8,2,1]
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [1,3,2,4,5,6]
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [1,2,3,6,5,4,7]
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [3,2,4,1,6,5,7]
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [2,3,1,7,6,5,4,8]
[3,3,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [2,1,8,7,6,5,4,3,9]
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1]
[3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [3,2,4,7,6,5,8,1]
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [3,2,1,4,6,5,7]
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [2,1,3,7,6,5,4,8]
[2,2,2,1,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [1,2,8,7,6,5,4,3,9]
[2,2,1,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [1,9,8,7,6,5,4,3,2,10]
[2,1,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [10,9,8,7,6,5,4,3,2,11,1]
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11]
[10,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [11,10,12,9,8,7,6,5,4,3,2,1] => [11,10,12,9,8,7,6,5,4,3,2,1]
[9,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [8,7,9,10,6,5,4,3,2,1]
[8,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [7,8,9,10,6,5,4,3,2,1]
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [6,5,4,3,7,8,2,1]
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7]
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [5,4,3,2,7,6,8,1]
[6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,2,1] => [5,6,4,3,7,8,2,1]
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,6,9,2,1] => [5,4,3,8,7,6,9,2,1]
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [4,5,6,7,8,3,2,1]
[6,2,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [6,5,7,8,9,4,3,2,1]
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7]
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [4,3,2,1,7,6,5,8]
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1]
[5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,8,1] => [4,5,3,2,7,6,8,1]
[5,4,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,5,9,1] => [4,3,2,8,7,6,5,9,1]
[5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [3,4,5,7,6,8,2,1]
[5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,2,1] => [5,4,6,3,7,8,2,1]
[5,3,2,1,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,6,9,2,1] => [4,5,3,8,7,6,9,2,1]
[5,2,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,5,4,6,7,9,3,2,1] => [5,4,6,8,7,9,3,2,1]
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6]
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [2,3,4,1,6,5,7]
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7]
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [3,4,2,1,7,6,5,8]
[4,4,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [3,2,1,8,7,6,5,4,9]
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [2,4,3,5,6,7,1]
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [2,3,4,7,6,5,8,1]
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [4,3,5,2,7,6,8,1]
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [5,4,3,6,7,8,2,1]
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6]
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [1,3,2,4,6,5,7]
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [1,2,3,7,6,5,4,8]
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7]
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [3,2,4,1,7,6,5,8]
[3,3,2,1,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => [2,3,1,8,7,6,5,4,9]
[3,3,1,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [2,1,9,8,7,6,5,4,3,10]
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [4,3,2,5,7,6,8,1]
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7]
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [3,2,1,4,7,6,5,8]
[2,2,2,1,1,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,1,2,3,10] => [1,2,9,8,7,6,5,4,3,10]
[2,1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11,10,9,8,7,6,5,4,3,2,12,1] => [11,10,9,8,7,6,5,4,3,2,12,1]
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [6,5,4,3,2,7,8,1]
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [5,6,7,8,9,4,3,2,1]
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [5,4,3,2,1,7,6,8]
[6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,2,1] => [4,5,6,3,7,8,2,1]
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7]
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [4,5,3,2,1,7,6,8]
[5,5,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => [4,3,2,1,8,7,6,5,9]
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1]
[5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,6,8,1] => [3,4,5,2,7,6,8,1]
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [5,4,6,3,2,7,8,1]
[5,4,2,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,6,9,1] => [4,5,3,2,8,7,6,9,1]
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [3,5,4,6,7,8,2,1]
[5,3,3,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8,7,3,4,5,6,9,2,1] => [3,4,5,8,7,6,9,2,1]
[5,3,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,6,3,7,9,2,1] => [5,4,6,3,8,7,9,2,1]
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [2,1,3,4,6,5,7]
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [2,4,3,5,1,6,7]
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [2,3,4,1,7,6,5,8]
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [4,3,5,2,1,7,6,8]
[4,4,2,1,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8,7,6,3,4,2,1,5,9] => [3,4,2,1,8,7,6,5,9]
[4,4,1,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [3,2,1,9,8,7,6,5,4,10]
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1]
[4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,8,1] => [2,4,3,5,7,6,8,1]
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [5,4,3,6,2,7,8,1]
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [1,2,3,4,6,5,7]
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [1,4,3,2,5,6,7]
[3,3,3,2,1,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [7,6,3,1,2,4,5,8] => [1,3,2,4,7,6,5,8]
[3,3,3,1,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,1,2,3,4,9] => [1,2,3,8,7,6,5,4,9]
[3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,1,6,8] => [4,3,2,5,1,7,6,8]
[3,3,1,1,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,2,1,3,11] => [2,1,10,9,8,7,6,5,4,3,11]
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,8,1]
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [4,3,2,1,5,7,6,8]
[8,3,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [6,7,8,9,10,5,4,3,2,1]
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7,8]
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [6,5,4,3,2,8,7,9,1]
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [5,6,4,3,2,1,7,8]
[6,6,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => [5,4,3,2,1,8,7,6,9]
[6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [4,5,6,3,2,7,8,1]
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,8,2,1]
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7]
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [3,4,5,2,1,7,6,8]
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [5,4,6,3,2,1,7,8]
[5,5,2,1,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8,7,4,5,3,2,1,6,9] => [4,5,3,2,1,8,7,6,9]
[5,5,1,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => [4,3,2,1,9,8,7,6,5,10]
[5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [3,2,4,5,7,6,8,1]
[5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,8,1] => [3,5,4,6,2,7,8,1]
[5,4,3,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8,7,3,4,5,2,6,9,1] => [3,4,5,2,8,7,6,9,1]
[5,4,2,2,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,6,3,2,7,9,1] => [5,4,6,3,2,8,7,9,1]
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [3,4,5,6,7,8,2,1]
[5,3,3,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8,5,3,4,6,7,9,2,1] => [3,5,4,6,8,7,9,2,1]
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [2,1,4,3,5,6,7]
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7]
[4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [2,4,3,5,1,7,6,8]
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [5,4,3,6,2,1,7,8]
[4,4,1,1,1,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,3,2,1,4,11] => [3,2,1,10,9,8,7,6,5,4,11]
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [2,3,4,5,7,6,8,1]
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [2,5,4,3,6,7,8,1]
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [1,2,4,3,5,6,7]
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [1,2,3,4,7,6,5,8]
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [1,4,3,2,5,7,6,8]
[3,3,3,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,1,2,3,4,10] => [1,2,3,9,8,7,6,5,4,10]
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7,8]
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7,8]
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [7,6,5,4,3,2,8,9,1]
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [6,5,4,3,2,1,8,7,9]
[7,4,4] => [1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [5,4,6,7,8,9,3,2,1]
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [4,5,6,3,2,1,7,8]
[6,6,2,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8,5,6,4,3,2,1,7,9] => [5,6,4,3,2,1,8,7,9]
[6,6,1,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [5,4,3,2,1,9,8,7,6,10]
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [4,3,5,6,2,7,8,1]
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [4,5,6,7,8,9,3,2,1]
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7]
[5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,1,6,8] => [3,2,4,5,1,7,6,8]
[5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,1,7,8] => [3,5,4,6,2,1,7,8]
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [3,2,5,4,6,7,8,1]
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [3,4,5,6,2,7,8,1]
[5,4,3,2,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8,5,3,4,6,2,7,9,1] => [3,5,4,6,2,8,7,9,1]
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7]
[4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [7,4,2,1,3,5,6,8] => [2,1,4,3,5,7,6,8]
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [2,3,4,5,1,7,6,8]
[4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,1,7,8] => [2,5,4,3,6,1,7,8]
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [2,3,5,4,6,7,8,1]
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7]
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [1,2,4,3,5,7,6,8]
[3,3,3,3,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [8,7,6,1,2,3,4,5,9] => [1,2,3,4,8,7,6,5,9]
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [1,5,4,3,2,6,7,8]
[3,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [6,5,4,3,2,7,8,9,1]
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [7,6,5,4,3,2,1,8,9]
[8,4,4] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [6,5,7,8,9,10,4,3,2,1]
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [6,7,5,4,3,2,1,8,9] => [6,7,5,4,3,2,1,8,9]
[7,7,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [6,5,4,3,2,1,9,8,7,10]
[7,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [5,6,7,8,9,10,4,3,2,1]
[6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,1,7,8] => [4,3,5,6,2,1,7,8]
[6,6,1,1,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,5,4,3,2,1,6,11] => [5,4,3,2,1,10,9,8,7,6,11]
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,8,1]
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [3,2,1,4,5,7,6,8]
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [3,2,5,4,6,1,7,8]
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [3,4,5,6,2,1,7,8]
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [3,4,2,5,6,7,8,1]
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [2,3,1,4,5,7,6,8]
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [2,1,5,4,3,6,7,8]
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [2,3,5,4,6,1,7,8]
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1]
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => [2,6,5,4,3,7,8,9,1]
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [2,1,3,4,5,7,6,8]
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [1,2,5,4,3,6,7,8]
[3,3,3,3,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => [1,2,3,4,9,8,7,6,5,10]
[3,3,2,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => [6,5,4,3,2,7,1,8,9]
[2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [6,5,4,3,2,1,7,8,9]
[9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,10,1] => [8,7,6,5,4,3,2,9,10,1]
[8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [7,6,5,4,3,2,1,9,8,10]
[7,7,1,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [10,9,8,6,5,4,3,2,1,7,11] => [6,5,4,3,2,1,10,9,8,7,11]
[7,5,5] => [1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,4,3,6,7,8,9,2,1] => [5,4,3,6,7,8,9,2,1]
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [4,3,2,5,6,1,7,8]
[6,4,4,3] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [4,5,3,6,7,8,9,2,1] => [4,5,3,6,7,8,9,2,1]
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [3,2,1,5,4,6,7,8]
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [3,4,2,5,6,1,7,8]
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1]
[5,3,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,2,1] => [4,3,5,6,7,8,9,2,1]
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [1,2,3,4,5,7,6,8]
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [2,3,1,5,4,6,7,8]
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [3,2,4,5,6,1,7,8]
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [2,1,3,5,4,6,7,8]
[3,3,3,2,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [1,6,5,4,3,2,7,8,9]
[3,2,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,8,9,10,1] => [7,6,5,4,3,2,8,9,10,1]
[] => [] => [] => []
[6,5,4,2,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [9,6,4,3,5,7,2,8,10,1] => [4,3,6,5,7,2,9,8,10,1]
[6,5,4,3,3,2,1] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [11,8,5,4,6,3,7,9,2,10,12,1] => [5,4,6,3,8,7,9,2,11,10,12,1]
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => [1,3,2,4,5,6,8,7,9]
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [2,4,3,5,6,7,8,9,1]
[7,3,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,5,7,8,9,10,11,4,3,2,1] => [6,5,7,8,9,10,11,4,3,2,1]
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [1,2,3,5,4,6,7,8]
[6,5,5,4] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,6,7,8,9,1] => [3,4,5,2,6,7,8,9,1]
[2,2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [7,6,5,4,3,2,1,8,9,10]
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8]
[3,3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [5,4,3,2,1,6,7,8,9,10]
[3,3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [8,3,2,1,4,5,6,7,9] => [3,2,1,4,5,6,8,7,9]
[3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [4,3,2,1,5,6,7,8,9]
[4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [4,3,2,5,6,7,8,9,1]
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8]
[4,4,4,3,3,3] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => [4,3,2,5,1,6,7,8,9]
[4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9]
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8]
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [3,2,1,4,5,6,7,8,9]
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7,8]
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [5,4,3,2,6,7,8,9,1]
[10,10] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9,8,7,6,5,4,3,2,1,10,11] => [9,8,7,6,5,4,3,2,1,10,11]
[6,6,6,6,6] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10]
[5,5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10]
[7,7,7,7] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [4,3,2,1,5,6,7,8,9,10]
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [5,4,3,2,1,6,7,8,9]
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9]
[9,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [8,7,6,5,4,3,2,1,9,10]
[8,8,8] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [6,5,4,3,2,1,7,8,9,10]
[4,4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [3,2,1,4,5,6,7,8,9,10]
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [3,2,4,5,6,7,8,9,1]
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [2,3,4,5,6,7,8,9,1]
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [1,2,3,4,5,6,8,7,9]
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [2,1,3,4,5,6,8,7,9]
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.