// output of ./demo/comb/perm-genus-demo.cc: // Description: //% Genus of all permutations of n elements. //% Print parenthesis strings for permutations of genus zero. //% Cf. OEIS sequence A177267. arg 1: 4 == n [Permutations of n elements.] default=4 1: [ . 1 2 3 ] 0 (0) (1) (2) (3) 1.1.1.1. [ . . . . ] 2: [ . 1 3 2 ] 0 (0) (1) (2, 3) 1.1.11.. [ . . . 1 ] 3: [ . 2 1 3 ] 0 (0) (1, 2) (3) 1.11..1. [ . . 1 . ] 4: [ . 2 3 1 ] 0 (0) (1, 2, 3) 1.11.1.. [ . . 1 1 ] 5: [ . 3 1 2 ] 1 (0) (1, 3, 2) 6: [ . 3 2 1 ] 0 (0) (1, 3) (2) 1.111... [ . . 1 2 ] 7: [ 1 . 2 3 ] 0 (0, 1) (2) (3) 11..1.1. [ . 1 . . ] 8: [ 1 . 3 2 ] 0 (0, 1) (2, 3) 11..11.. [ . 1 . 1 ] 9: [ 1 2 . 3 ] 0 (0, 1, 2) (3) 11.1..1. [ . 1 1 . ] 10: [ 1 2 3 . ] 0 (0, 1, 2, 3) 11.1.1.. [ . 1 1 1 ] 11: [ 1 3 . 2 ] 1 (0, 1, 3, 2) 12: [ 1 3 2 . ] 0 (0, 1, 3) (2) 11.11... [ . 1 1 2 ] 13: [ 2 . 1 3 ] 1 (0, 2, 1) (3) 14: [ 2 . 3 1 ] 1 (0, 2, 3, 1) 15: [ 2 1 . 3 ] 0 (0, 2) (1) (3) 111...1. [ . 1 2 . ] 16: [ 2 1 3 . ] 0 (0, 2, 3) (1) 111..1.. [ . 1 2 1 ] 17: [ 2 3 . 1 ] 1 (0, 2) (1, 3) 18: [ 2 3 1 . ] 1 (0, 2, 1, 3) 19: [ 3 . 1 2 ] 1 (0, 3, 2, 1) 20: [ 3 . 2 1 ] 1 (0, 3, 1) (2) 21: [ 3 1 . 2 ] 1 (0, 3, 2) (1) 22: [ 3 1 2 . ] 0 (0, 3) (1) (2) 111.1... [ . 1 2 2 ] 23: [ 3 2 . 1 ] 1 (0, 3, 1, 2) 24: [ 3 2 1 . ] 0 (0, 3) (1, 2) 1111.... [ . 1 2 3 ] ct=24 14, 10, 0, 0,