// output of ./demo/comb/setpart-rgs-subset-lex-demo.cc: // Description: //% Set partitions of the n-set as restricted growth strings (RGS): //% strings s[0, 1, ..., n-1] such that s[k] <= max(s[0], s[1], ..., s[k-1]) + 1. //% Subset-lex order. //% See Joerg Arndt, Subset-lex: did we miss an order?, (2014) //% http://arxiv.org/abs/1405.6503 arg 1: 5 == n [Length of RGS] default=5 arg 2: 0 == bw [Whether to generate backward order] default=0 0: [ . . . . . ] 1 [ 1 1 1 1 1 ] {1, 2, 3, 4, 5} 1: [ . 1 . . . ] 1 [ 1 1 1 1 1 ] {1, 3, 4, 5}, {2} 2: [ . 1 1 . . ] 2 [ 1 1 2 1 1 ] {1, 4, 5}, {2, 3} 3: [ . 1 2 . . ] 2 [ 1 1 2 1 1 ] {1, 4, 5}, {2}, {3} 4: [ . 1 2 1 . ] 3 [ 1 1 2 3 1 ] {1, 5}, {2, 4}, {3} 5: [ . 1 2 2 . ] 3 [ 1 1 2 3 1 ] {1, 5}, {2}, {3, 4} 6: [ . 1 2 3 . ] 3 [ 1 1 2 3 1 ] {1, 5}, {2}, {3}, {4} 7: [ . 1 2 3 1 ] 4 [ 1 1 2 3 4 ] {1}, {2, 5}, {3}, {4} 8: [ . 1 2 3 2 ] 4 [ 1 1 2 3 4 ] {1}, {2}, {3, 5}, {4} 9: [ . 1 2 3 3 ] 4 [ 1 1 2 3 4 ] {1}, {2}, {3}, {4, 5} 10: [ . 1 2 3 4 ] 4 [ 1 1 2 3 4 ] {1}, {2}, {3}, {4}, {5} 11: [ . 1 2 2 1 ] 4 [ 1 1 2 3 3 ] {1}, {2, 5}, {3, 4} 12: [ . 1 2 2 2 ] 4 [ 1 1 2 3 3 ] {1}, {2}, {3, 4, 5} 13: [ . 1 2 2 3 ] 4 [ 1 1 2 3 3 ] {1}, {2}, {3, 4}, {5} 14: [ . 1 2 1 1 ] 4 [ 1 1 2 3 3 ] {1}, {2, 4, 5}, {3} 15: [ . 1 2 1 2 ] 4 [ 1 1 2 3 3 ] {1}, {2, 4}, {3, 5} 16: [ . 1 2 1 3 ] 4 [ 1 1 2 3 3 ] {1}, {2, 4}, {3}, {5} 17: [ . 1 2 . 1 ] 4 [ 1 1 2 3 3 ] {1, 4}, {2, 5}, {3} 18: [ . 1 2 . 2 ] 4 [ 1 1 2 3 3 ] {1, 4}, {2}, {3, 5} 19: [ . 1 2 . 3 ] 4 [ 1 1 2 3 3 ] {1, 4}, {2}, {3}, {5} 20: [ . 1 1 1 . ] 3 [ 1 1 2 2 3 ] {1, 5}, {2, 3, 4} 21: [ . 1 1 2 . ] 3 [ 1 1 2 2 3 ] {1, 5}, {2, 3}, {4} 22: [ . 1 1 2 1 ] 4 [ 1 1 2 2 3 ] {1}, {2, 3, 5}, {4} 23: [ . 1 1 2 2 ] 4 [ 1 1 2 2 3 ] {1}, {2, 3}, {4, 5} 24: [ . 1 1 2 3 ] 4 [ 1 1 2 2 3 ] {1}, {2, 3}, {4}, {5} 25: [ . 1 1 1 1 ] 4 [ 1 1 2 2 2 ] {1}, {2, 3, 4, 5} 26: [ . 1 1 1 2 ] 4 [ 1 1 2 2 2 ] {1}, {2, 3, 4}, {5} 27: [ . 1 1 . 1 ] 4 [ 1 1 2 2 2 ] {1, 4}, {2, 3, 5} 28: [ . 1 1 . 2 ] 4 [ 1 1 2 2 2 ] {1, 4}, {2, 3}, {5} 29: [ . 1 . 1 . ] 3 [ 1 1 2 2 2 ] {1, 3, 5}, {2, 4} 30: [ . 1 . 2 . ] 3 [ 1 1 2 2 2 ] {1, 3, 5}, {2}, {4} 31: [ . 1 . 2 1 ] 4 [ 1 1 2 2 3 ] {1, 3}, {2, 5}, {4} 32: [ . 1 . 2 2 ] 4 [ 1 1 2 2 3 ] {1, 3}, {2}, {4, 5} 33: [ . 1 . 2 3 ] 4 [ 1 1 2 2 3 ] {1, 3}, {2}, {4}, {5} 34: [ . 1 . 1 1 ] 4 [ 1 1 2 2 2 ] {1, 3}, {2, 4, 5} 35: [ . 1 . 1 2 ] 4 [ 1 1 2 2 2 ] {1, 3}, {2, 4}, {5} 36: [ . 1 . . 1 ] 4 [ 1 1 2 2 2 ] {1, 3, 4}, {2, 5} 37: [ . 1 . . 2 ] 4 [ 1 1 2 2 2 ] {1, 3, 4}, {2}, {5} 38: [ . . 1 . . ] 2 [ 1 1 1 2 2 ] {1, 2, 4, 5}, {3} 39: [ . . 1 1 . ] 3 [ 1 1 1 2 2 ] {1, 2, 5}, {3, 4} 40: [ . . 1 2 . ] 3 [ 1 1 1 2 2 ] {1, 2, 5}, {3}, {4} 41: [ . . 1 2 1 ] 4 [ 1 1 1 2 3 ] {1, 2}, {3, 5}, {4} 42: [ . . 1 2 2 ] 4 [ 1 1 1 2 3 ] {1, 2}, {3}, {4, 5} 43: [ . . 1 2 3 ] 4 [ 1 1 1 2 3 ] {1, 2}, {3}, {4}, {5} 44: [ . . 1 1 1 ] 4 [ 1 1 1 2 2 ] {1, 2}, {3, 4, 5} 45: [ . . 1 1 2 ] 4 [ 1 1 1 2 2 ] {1, 2}, {3, 4}, {5} 46: [ . . 1 . 1 ] 4 [ 1 1 1 2 2 ] {1, 2, 4}, {3, 5} 47: [ . . 1 . 2 ] 4 [ 1 1 1 2 2 ] {1, 2, 4}, {3}, {5} 48: [ . . . 1 . ] 3 [ 1 1 1 1 2 ] {1, 2, 3, 5}, {4} 49: [ . . . 1 1 ] 4 [ 1 1 1 1 2 ] {1, 2, 3}, {4, 5} 50: [ . . . 1 2 ] 4 [ 1 1 1 1 2 ] {1, 2, 3}, {4}, {5} 51: [ . . . . 1 ] 4 [ 1 1 1 1 1 ] {1, 2, 3, 4}, {5} ct=52