// output of ./demo/comb/cayley-perm-demo.cc: // Description: //% Cayley permutations: Length-n words such that all elements //% from 0 to the maximum value occur at least once. //% Same as: permutations of the (RGS for) set partitions of n. //% Same as: weak orders on n elements (weak orders are //% relations that are transitive and complete). //% Same as: preferential arrangements of n labeled elements. //% Generation such that the major order is by content, and minor order lexicographic. //% Cf. OEIS sequence A000670 (Fubini numbers). arg 1: 4 == n [Length of words] default=4 arg 2: 0 == mi [Minimal value of max digit] default=0 arg 3: 3 == mx [Max allowed digit] default=3 1: [ . . . . ] 0 { 0, 1, 2, 3 } 2: [ . . . 1 ] 1 { 0, 1, 2 } < { 3 } 3: [ . . 1 . ] 1 { 0, 1, 3 } < { 2 } 4: [ . 1 . . ] 1 { 0, 2, 3 } < { 1 } 5: [ 1 . . . ] 1 { 1, 2, 3 } < { 0 } 6: [ . . 1 1 ] 1 { 0, 1 } < { 2, 3 } 7: [ . 1 . 1 ] 1 { 0, 2 } < { 1, 3 } 8: [ . 1 1 . ] 1 { 0, 3 } < { 1, 2 } 9: [ 1 . . 1 ] 1 { 1, 2 } < { 0, 3 } 10: [ 1 . 1 . ] 1 { 1, 3 } < { 0, 2 } 11: [ 1 1 . . ] 1 { 2, 3 } < { 0, 1 } 12: [ . . 1 2 ] 2 { 0, 1 } < { 2 } < { 3 } 13: [ . . 2 1 ] 2 { 0, 1 } < { 3 } < { 2 } 14: [ . 1 . 2 ] 2 { 0, 2 } < { 1 } < { 3 } 15: [ . 1 2 . ] 2 { 0, 3 } < { 1 } < { 2 } 16: [ . 2 . 1 ] 2 { 0, 2 } < { 3 } < { 1 } 17: [ . 2 1 . ] 2 { 0, 3 } < { 2 } < { 1 } 18: [ 1 . . 2 ] 2 { 1, 2 } < { 0 } < { 3 } 19: [ 1 . 2 . ] 2 { 1, 3 } < { 0 } < { 2 } 20: [ 1 2 . . ] 2 { 2, 3 } < { 0 } < { 1 } 21: [ 2 . . 1 ] 2 { 1, 2 } < { 3 } < { 0 } 22: [ 2 . 1 . ] 2 { 1, 3 } < { 2 } < { 0 } 23: [ 2 1 . . ] 2 { 2, 3 } < { 1 } < { 0 } 24: [ . 1 1 1 ] 1 { 0 } < { 1, 2, 3 } 25: [ 1 . 1 1 ] 1 { 1 } < { 0, 2, 3 } 26: [ 1 1 . 1 ] 1 { 2 } < { 0, 1, 3 } 27: [ 1 1 1 . ] 1 { 3 } < { 0, 1, 2 } 28: [ . 1 1 2 ] 2 { 0 } < { 1, 2 } < { 3 } 29: [ . 1 2 1 ] 2 { 0 } < { 1, 3 } < { 2 } 30: [ . 2 1 1 ] 2 { 0 } < { 2, 3 } < { 1 } 31: [ 1 . 1 2 ] 2 { 1 } < { 0, 2 } < { 3 } 32: [ 1 . 2 1 ] 2 { 1 } < { 0, 3 } < { 2 } 33: [ 1 1 . 2 ] 2 { 2 } < { 0, 1 } < { 3 } 34: [ 1 1 2 . ] 2 { 3 } < { 0, 1 } < { 2 } 35: [ 1 2 . 1 ] 2 { 2 } < { 0, 3 } < { 1 } 36: [ 1 2 1 . ] 2 { 3 } < { 0, 2 } < { 1 } 37: [ 2 . 1 1 ] 2 { 1 } < { 2, 3 } < { 0 } 38: [ 2 1 . 1 ] 2 { 2 } < { 1, 3 } < { 0 } 39: [ 2 1 1 . ] 2 { 3 } < { 1, 2 } < { 0 } 40: [ . 1 2 2 ] 2 { 0 } < { 1 } < { 2, 3 } 41: [ . 2 1 2 ] 2 { 0 } < { 2 } < { 1, 3 } 42: [ . 2 2 1 ] 2 { 0 } < { 3 } < { 1, 2 } 43: [ 1 . 2 2 ] 2 { 1 } < { 0 } < { 2, 3 } 44: [ 1 2 . 2 ] 2 { 2 } < { 0 } < { 1, 3 } 45: [ 1 2 2 . ] 2 { 3 } < { 0 } < { 1, 2 } 46: [ 2 . 1 2 ] 2 { 1 } < { 2 } < { 0, 3 } 47: [ 2 . 2 1 ] 2 { 1 } < { 3 } < { 0, 2 } 48: [ 2 1 . 2 ] 2 { 2 } < { 1 } < { 0, 3 } 49: [ 2 1 2 . ] 2 { 3 } < { 1 } < { 0, 2 } 50: [ 2 2 . 1 ] 2 { 2 } < { 3 } < { 0, 1 } 51: [ 2 2 1 . ] 2 { 3 } < { 2 } < { 0, 1 } 52: [ . 1 2 3 ] 3 { 0 } < { 1 } < { 2 } < { 3 } 53: [ . 1 3 2 ] 3 { 0 } < { 1 } < { 3 } < { 2 } 54: [ . 2 1 3 ] 3 { 0 } < { 2 } < { 1 } < { 3 } 55: [ . 2 3 1 ] 3 { 0 } < { 3 } < { 1 } < { 2 } 56: [ . 3 1 2 ] 3 { 0 } < { 2 } < { 3 } < { 1 } 57: [ . 3 2 1 ] 3 { 0 } < { 3 } < { 2 } < { 1 } 58: [ 1 . 2 3 ] 3 { 1 } < { 0 } < { 2 } < { 3 } 59: [ 1 . 3 2 ] 3 { 1 } < { 0 } < { 3 } < { 2 } 60: [ 1 2 . 3 ] 3 { 2 } < { 0 } < { 1 } < { 3 } 61: [ 1 2 3 . ] 3 { 3 } < { 0 } < { 1 } < { 2 } 62: [ 1 3 . 2 ] 3 { 2 } < { 0 } < { 3 } < { 1 } 63: [ 1 3 2 . ] 3 { 3 } < { 0 } < { 2 } < { 1 } 64: [ 2 . 1 3 ] 3 { 1 } < { 2 } < { 0 } < { 3 } 65: [ 2 . 3 1 ] 3 { 1 } < { 3 } < { 0 } < { 2 } 66: [ 2 1 . 3 ] 3 { 2 } < { 1 } < { 0 } < { 3 } 67: [ 2 1 3 . ] 3 { 3 } < { 1 } < { 0 } < { 2 } 68: [ 2 3 . 1 ] 3 { 2 } < { 3 } < { 0 } < { 1 } 69: [ 2 3 1 . ] 3 { 3 } < { 2 } < { 0 } < { 1 } 70: [ 3 . 1 2 ] 3 { 1 } < { 2 } < { 3 } < { 0 } 71: [ 3 . 2 1 ] 3 { 1 } < { 3 } < { 2 } < { 0 } 72: [ 3 1 . 2 ] 3 { 2 } < { 1 } < { 3 } < { 0 } 73: [ 3 1 2 . ] 3 { 3 } < { 1 } < { 2 } < { 0 } 74: [ 3 2 . 1 ] 3 { 2 } < { 3 } < { 1 } < { 0 } 75: [ 3 2 1 . ] 3 { 3 } < { 2 } < { 1 } < { 0 } ct=75