// output of ./demo/comb/binary-necklace-demo.cc: // Description: //% Binary pre-necklaces, necklaces, and Lyndon words: CAT generation. //% Cf. OEIS sequences A062692 (pre-necklaces), A000031 (necklaces), //% and A001037 (Lyndon words). arg 1: 8 == n [Number of bits] default=8 1: ........ 1 N 2: .......1 8 N L 3: ......1. 7 4: ......11 8 N L 5: .....1.. 6 6: .....1.1 8 N L 7: .....11. 7 8: .....111 8 N L 9: ....1... 5 10: ....1..1 8 N L 11: ....1.1. 7 12: ....1.11 8 N L 13: ....11.. 6 14: ....11.1 8 N L 15: ....111. 7 16: ....1111 8 N L 17: ...1...1 4 N 18: ...1..1. 7 19: ...1..11 8 N L 20: ...1.1.. 6 21: ...1.1.1 8 N L 22: ...1.11. 7 23: ...1.111 8 N L 24: ...11... 5 25: ...11..1 8 N L 26: ...11.1. 7 27: ...11.11 8 N L 28: ...111.. 6 29: ...111.1 8 N L 30: ...1111. 7 31: ...11111 8 N L 32: ..1..1.. 3 33: ..1..1.1 8 N L 34: ..1..11. 7 35: ..1..111 8 N L 36: ..1.1..1 5 37: ..1.1.1. 7 38: ..1.1.11 8 N L 39: ..1.11.. 6 40: ..1.11.1 8 N L 41: ..1.111. 7 42: ..1.1111 8 N L 43: ..11..11 4 N 44: ..11.1.. 6 45: ..11.1.1 8 N L 46: ..11.11. 7 47: ..11.111 8 N L 48: ..111..1 5 49: ..111.1. 7 50: ..111.11 8 N L 51: ..1111.. 6 52: ..1111.1 8 N L 53: ..11111. 7 54: ..111111 8 N L 55: .1.1.1.1 2 N 56: .1.1.11. 7 57: .1.1.111 8 N L 58: .1.11.1. 5 59: .1.11.11 8 N L 60: .1.111.1 6 61: .1.1111. 7 62: .1.11111 8 N L 63: .11.11.1 3 64: .11.111. 7 65: .11.1111 8 N L 66: .111.111 4 N 67: .1111.11 5 68: .11111.1 6 69: .111111. 7 70: .1111111 8 N L 71: 11111111 1 N n = 8: # pre-necklaces = 71 # necklaces = 36 # Lyndon words = 30