// output of ./demo/comb/subset-lex-demo.cc: // Description: //% Nonempty subsets of the set {0,1,2,...,n-1} in (subset-)lexicographic order. //% Representation as list of parts. //% Loopless generation. //% Cf. OEIS sequence A108918 //% See Joerg Arndt, Subset-lex: did we miss an order?, (2014) //% http://arxiv.org/abs/1405.6503 arg 1: 6 == n [Size of the set (n>=1)] default=6 1: 1..... { 0 } 2: 11.... { 0, 1 } 3: 111... { 0, 1, 2 } 4: 1111.. { 0, 1, 2, 3 } 5: 11111. { 0, 1, 2, 3, 4 } 6: 111111 { 0, 1, 2, 3, 4, 5 } 7: 1111.1 { 0, 1, 2, 3, 5 } 8: 111.1. { 0, 1, 2, 4 } 9: 111.11 { 0, 1, 2, 4, 5 } 10: 111..1 { 0, 1, 2, 5 } 11: 11.1.. { 0, 1, 3 } 12: 11.11. { 0, 1, 3, 4 } 13: 11.111 { 0, 1, 3, 4, 5 } 14: 11.1.1 { 0, 1, 3, 5 } 15: 11..1. { 0, 1, 4 } 16: 11..11 { 0, 1, 4, 5 } 17: 11...1 { 0, 1, 5 } 18: 1.1... { 0, 2 } 19: 1.11.. { 0, 2, 3 } 20: 1.111. { 0, 2, 3, 4 } 21: 1.1111 { 0, 2, 3, 4, 5 } 22: 1.11.1 { 0, 2, 3, 5 } 23: 1.1.1. { 0, 2, 4 } 24: 1.1.11 { 0, 2, 4, 5 } 25: 1.1..1 { 0, 2, 5 } 26: 1..1.. { 0, 3 } 27: 1..11. { 0, 3, 4 } 28: 1..111 { 0, 3, 4, 5 } 29: 1..1.1 { 0, 3, 5 } 30: 1...1. { 0, 4 } 31: 1...11 { 0, 4, 5 } 32: 1....1 { 0, 5 } 33: .1.... { 1 } 34: .11... { 1, 2 } 35: .111.. { 1, 2, 3 } 36: .1111. { 1, 2, 3, 4 } 37: .11111 { 1, 2, 3, 4, 5 } 38: .111.1 { 1, 2, 3, 5 } 39: .11.1. { 1, 2, 4 } 40: .11.11 { 1, 2, 4, 5 } 41: .11..1 { 1, 2, 5 } 42: .1.1.. { 1, 3 } 43: .1.11. { 1, 3, 4 } 44: .1.111 { 1, 3, 4, 5 } 45: .1.1.1 { 1, 3, 5 } 46: .1..1. { 1, 4 } 47: .1..11 { 1, 4, 5 } 48: .1...1 { 1, 5 } 49: ..1... { 2 } 50: ..11.. { 2, 3 } 51: ..111. { 2, 3, 4 } 52: ..1111 { 2, 3, 4, 5 } 53: ..11.1 { 2, 3, 5 } 54: ..1.1. { 2, 4 } 55: ..1.11 { 2, 4, 5 } 56: ..1..1 { 2, 5 } 57: ...1.. { 3 } 58: ...11. { 3, 4 } 59: ...111 { 3, 4, 5 } 60: ...1.1 { 3, 5 } 61: ....1. { 4 } 62: ....11 { 4, 5 } 63: .....1 { 5 }