Identifier
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Images
[1] => [1,0] => [1]
[2] => [1,0,1,0] => [1,1]
[1,1] => [1,1,0,0] => [2]
[3] => [1,0,1,0,1,0] => [1,1,1]
[2,1] => [1,0,1,1,0,0] => [1,2]
[1,1,1] => [1,1,0,1,0,0] => [3]
[4] => [1,0,1,0,1,0,1,0] => [1,1,1,1]
[3,1] => [1,0,1,0,1,1,0,0] => [1,1,2]
[2,2] => [1,1,1,0,0,0] => [3]
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,3]
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [4]
[5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1]
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,2]
[3,2] => [1,0,1,1,1,0,0,0] => [1,3]
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,3]
[2,2,1] => [1,1,1,0,0,1,0,0] => [4]
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,4]
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [5]
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1]
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2]
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,3]
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3]
[3,3] => [1,1,1,0,1,0,0,0] => [4]
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [1,4]
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4]
[2,2,2] => [1,1,1,1,0,0,0,0] => [4]
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [5]
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,5]
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [6]
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1]
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2]
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3]
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3]
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,4]
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4]
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4]
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [5]
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [1,4]
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,5]
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5]
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [5]
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [6]
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6]
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7]
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1]
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2]
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3]
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3]
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4]
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4]
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4]
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [5]
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,5]
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4]
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5]
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5]
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [5]
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [6]
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,5]
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6]
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6]
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [5]
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [6]
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7]
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,7]
[1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8]
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1]
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2]
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3]
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,3]
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4]
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4]
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4]
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,5]
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5]
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4]
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5]
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5]
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [6]
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,5]
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6]
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5]
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6]
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6]
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [5]
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [6]
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7]
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,5]
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6]
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,7]
[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] => [1,1,7]
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [6]
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7]
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [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] => [1,8]
[1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9]
[10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1]
[9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2]
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3]
[8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,3]
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4]
>>> Load all 444 entries. <<<
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4]
[7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,4]
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5]
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5]
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4]
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5]
[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] => [1,1,1,1,1,5]
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [6]
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6]
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5]
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6]
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5]
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6]
[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] => [1,1,1,1,6]
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [6]
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7]
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,5]
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6]
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,7]
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5]
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6]
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7]
[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] => [1,1,1,7]
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [6]
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [6]
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7]
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8]
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6]
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,7]
[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] => [1,8]
[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] => [1,1,8]
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [6]
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7]
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [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] => [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] => [1,9]
[1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10]
[11] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1]
[10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,2]
[9,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3]
[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] => [1,1,1,1,1,1,1,1,3]
[8,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4]
[8,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,1,4]
[8,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,1,4]
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5]
[7,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5]
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4]
[7,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,5]
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6]
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6]
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5]
[6,3,1,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6]
[6,2,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5]
[6,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,6]
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7]
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6]
[5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,7]
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5]
[5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6]
[5,3,1,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7]
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5]
[5,2,2,1,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6]
[5,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,7]
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [6]
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7]
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8]
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6]
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6]
[4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,7]
[4,3,1,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,8]
[4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6]
[4,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,8]
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [6]
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7]
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7]
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [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] => [9]
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6]
[3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,7]
[3,2,1,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9]
[3,1,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,9]
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7]
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [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] => [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] => [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] => [1,10]
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11]
[10,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,3]
[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] => [1,1,1,1,1,1,1,1,1,3]
[9,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,4]
[8,4] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5]
[8,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,5]
[8,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,4]
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6]
[7,4,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6]
[7,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5]
[7,3,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,6]
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7]
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,7]
[6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6]
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7]
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5]
[6,3,1,1,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,7]
[6,2,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5]
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7]
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8]
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6]
[5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,7]
[5,4,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,8]
[5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6]
[5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6]
[5,3,2,1,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7]
[5,3,1,1,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8]
[5,2,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6]
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [6]
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7]
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7]
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [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] => [9]
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6]
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,7]
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,7]
[4,3,1,1,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,9]
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6]
[4,2,2,2,1,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7]
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [6]
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7]
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8]
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7]
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [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] => [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] => [10]
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,7]
[3,2,2,2,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,8]
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7]
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8]
[2,2,2,2,1,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0] => [9]
[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] => [10]
[2,2,1,1,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [11]
[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] => [1,11]
[9,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,5]
[8,5] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6]
[8,3,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,5]
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,7]
[7,4,2] => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6]
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5]
[7,2,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,5]
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8]
[6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,7]
[6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6]
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7]
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8]
[5,5,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9]
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6]
[5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,7]
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,7]
[5,4,2,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,8]
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6]
[5,3,3,1,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7]
[5,3,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7]
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7]
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7]
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8]
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [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] => [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] => [10]
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6]
[4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,7]
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,7]
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7]
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7]
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7]
[3,3,3,2,1,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [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] => [9]
[3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [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] => [11]
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,7]
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8]
[2,2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9]
[9,5] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,6]
[8,6] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7]
[8,4,2] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,6]
[8,3,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5]
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8]
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [1,8]
[7,5,2] => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7]
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8]
[6,6,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9]
[6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,7]
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6]
[6,3,3,2] => [1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6]
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7]
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8]
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8]
[5,5,2,1,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [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] => [10]
[5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,7]
[5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,7]
[5,4,3,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,8]
[5,4,2,2,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [1,8]
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6]
[5,3,3,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7]
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7]
[4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8]
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7]
[4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8]
[4,4,3,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [9]
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8]
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7]
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,7]
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7]
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8]
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [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] => [10]
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8]
[3,2,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,8]
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8]
[2,2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0] => [9]
[9,6] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,7]
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,8]
[8,5,2] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,7]
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9]
[7,6,2] => [1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,8]
[7,4,4] => [1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6]
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8]
[6,6,2,1] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [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] => [10]
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,7]
[6,4,4,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7]
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6]
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7]
[5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8]
[5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8]
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,7]
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,7]
[5,4,3,2,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,8]
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7]
[4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8]
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8]
[4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8]
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7]
[4,3,3,3,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,8]
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7]
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [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] => [9]
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [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] => [1,8]
[2,2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0] => [9]
[2,2,2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0] => [10]
[9,7] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,8]
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [9]
[8,6,2] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8]
[8,4,4] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,6]
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [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] => [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] => [1,1,1,1,6]
[6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8]
[6,6,3,1] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [9]
[6,6,2,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [9]
[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] => [11]
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,7]
[6,4,3,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,8]
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8]
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8]
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8]
[5,5,2,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [9]
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,7]
[5,3,3,3,2] => [1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7]
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7]
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8]
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8]
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8]
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7]
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,8]
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8]
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [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] => [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] => [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] => [9]
[9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,9]
[8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [10]
[8,7,2] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,9]
[7,7,3] => [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [9]
[7,5,5] => [1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7]
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8]
[6,5,3,3] => [1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,8]
[6,4,4,3] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7]
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8]
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8]
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7]
[5,3,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7]
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8]
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8]
[4,4,4,3,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0] => [9]
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8]
[4,3,3,3,3,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,8]
[4,3,3,3,2,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,8]
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8]
[3,3,3,3,3,1,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0] => [9]
[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] => [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] => [1,9]
[] => [] => []
[5,5,4,3,2,1] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [10]
[5,5,4,2,1,1] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0] => [10]
[5,5,4,3,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [9]
[5,5,4,3,1] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [9]
[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] => [1,9]
[6,6,5,4,3,2,1] => [1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0] => [12]
[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] => [1,11]
[4,3,3,3,3,2] => [1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,8]
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [9]
[6,6,5,4,3] => [1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [10]
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8]
[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] => [1,1,1,1,7]
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8]
[6,5,5,4] => [1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,8]
[7,6,5] => [1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [1,8]
[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] => [10]
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [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] => [10]
[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] => [9]
[3,3,3,3,3,2,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [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] => [1,8]
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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] => [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] => [9]
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8]
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [9]
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8]
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,8]
[10,10] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [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] => [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] => [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] => [10]
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [9]
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9]
[9,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [10]
[8,8,8] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [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] => [10]
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8]
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8]
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9]
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [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
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.