// output of ./demo/comb/perm-involution-naf-demo.cc: // Description: //% Self-inverse permutations (involutions) from falling factorial numbers //% that are non-adjacent forms (NAF). //% Cf. OEIS sequence A000085. arg 1: 5 == n [Self-inverse permutations of n elements.] default=5 0: [ 4 . 2 . ] (0, 4) (1, 3) (2) [ 4 3 2 1 0 ] 1: [ 3 . 2 . ] (0, 3) (1, 4) (2) [ 3 4 2 0 1 ] 2: [ 2 . 2 . ] (0, 2) (1, 4) (3) [ 2 4 0 3 1 ] 3: [ 1 . 2 . ] (0, 1) (2, 4) (3) [ 1 0 4 3 2 ] 4: [ . . 2 . ] (0) (1) (2, 4) (3) [ 0 1 4 3 2 ] 5: [ . . 1 . ] (0) (1) (2, 3) (4) [ 0 1 3 2 4 ] 6: [ 1 . 1 . ] (0, 1) (2, 3) (4) [ 1 0 3 2 4 ] 7: [ 2 . 1 . ] (0, 2) (1, 3) (4) [ 2 3 0 1 4 ] 8: [ 3 . 1 . ] (0, 3) (1, 2) (4) [ 3 2 1 0 4 ] 9: [ 4 . 1 . ] (0, 4) (1, 2) (3) [ 4 2 1 3 0 ] 10: [ 4 . . . ] (0, 4) (1) (2) (3) [ 4 1 2 3 0 ] 11: [ 3 . . . ] (0, 3) (1) (2) (4) [ 3 1 2 0 4 ] 12: [ 2 . . . ] (0, 2) (1) (3) (4) [ 2 1 0 3 4 ] 13: [ 1 . . . ] (0, 1) (2) (3) (4) [ 1 0 2 3 4 ] 14: [ . . . . ] (0) (1) (2) (3) (4) [ 0 1 2 3 4 ] 15: [ . 1 . . ] (0) (1, 2) (3) (4) [ 0 2 1 3 4 ] 16: [ . 2 . . ] (0) (1, 3) (2) (4) [ 0 3 2 1 4 ] 17: [ . 3 . . ] (0) (1, 4) (2) (3) [ 0 4 2 3 1 ] 18: [ . 3 . 1 ] (0) (1, 4) (2, 3) [ 0 4 3 2 1 ] 19: [ . 2 . 1 ] (0) (1, 3) (2, 4) [ 0 3 4 1 2 ] 20: [ . 1 . 1 ] (0) (1, 2) (3, 4) [ 0 2 1 4 3 ] 21: [ . . . 1 ] (0) (1) (2) (3, 4) [ 0 1 2 4 3 ] 22: [ 1 . . 1 ] (0, 1) (2) (3, 4) [ 1 0 2 4 3 ] 23: [ 2 . . 1 ] (0, 2) (1) (3, 4) [ 2 1 0 4 3 ] 24: [ 3 . . 1 ] (0, 3) (1) (2, 4) [ 3 1 4 0 2 ] 25: [ 4 . . 1 ] (0, 4) (1) (2, 3) [ 4 1 3 2 0 ] ct=26