// output of ./demo/comb/setpart-p-rgs-lex-demo.cc: // Description: //% Set partitions of the n-set into p parts as restricted growth strings (RGS). //% Counted by the Stirling numbers of second kind S(n,p). //% Cf. OEIS sequence A008277. arg 1: 5 == n [Partition set of n elements] default=5 arg 2: 3 == p [Partitions into p parts (1<=p<=n)] default=3 1: [ . . . 1 2 ] {1, 2, 3}, {4}, {5} 2: [ . . 1 . 2 ] {1, 2, 4}, {3}, {5} 3: [ . . 1 1 2 ] {1, 2}, {3, 4}, {5} 4: [ . . 1 2 . ] {1, 2, 5}, {3}, {4} 5: [ . . 1 2 1 ] {1, 2}, {3, 5}, {4} 6: [ . . 1 2 2 ] {1, 2}, {3}, {4, 5} 7: [ . 1 . . 2 ] {1, 3, 4}, {2}, {5} 8: [ . 1 . 1 2 ] {1, 3}, {2, 4}, {5} 9: [ . 1 . 2 . ] {1, 3, 5}, {2}, {4} 10: [ . 1 . 2 1 ] {1, 3}, {2, 5}, {4} 11: [ . 1 . 2 2 ] {1, 3}, {2}, {4, 5} 12: [ . 1 1 . 2 ] {1, 4}, {2, 3}, {5} 13: [ . 1 1 1 2 ] {1}, {2, 3, 4}, {5} 14: [ . 1 1 2 . ] {1, 5}, {2, 3}, {4} 15: [ . 1 1 2 1 ] {1}, {2, 3, 5}, {4} 16: [ . 1 1 2 2 ] {1}, {2, 3}, {4, 5} 17: [ . 1 2 . . ] {1, 4, 5}, {2}, {3} 18: [ . 1 2 . 1 ] {1, 4}, {2, 5}, {3} 19: [ . 1 2 . 2 ] {1, 4}, {2}, {3, 5} 20: [ . 1 2 1 . ] {1, 5}, {2, 4}, {3} 21: [ . 1 2 1 1 ] {1}, {2, 4, 5}, {3} 22: [ . 1 2 1 2 ] {1}, {2, 4}, {3, 5} 23: [ . 1 2 2 . ] {1, 5}, {2}, {3, 4} 24: [ . 1 2 2 1 ] {1}, {2, 5}, {3, 4} 25: [ . 1 2 2 2 ] {1}, {2}, {3, 4, 5} ct=25