// output of ./demo/comb/dyck-pref-demo.cc: // Description: //% k-ary Dyck words via prefix shifts. //% Representation as delta set. //% Algorithm "coolkat" as given (left in figure "Algorithms 1") in //% Stephane Durocher, Pak Ching Li, Debajyoti Mondal, Aaron Williams: //% "Ranking and Loopless Generation of k-ary Dyck Words in Cool-lex Order", arg 1: 4 == n [Number of ones in words (n>=1).] default=4 arg 2: 3 == k [k-ary Dyck words (k>=1, k==2 gives Catalan strings).] default=3 1: 1111........ { 0, 1, 2, 3 } [ . 2 4 6 ] 2: 1.111....... { 0, 2, 3, 4 } [ . 1 3 5 ] 3: 11.11....... { 0, 1, 3, 4 } [ . 2 3 5 ] 4: 111.1....... { 0, 1, 2, 4 } [ . 2 4 5 ] 5: 1.11.1...... { 0, 2, 3, 5 } [ . 1 3 4 ] 6: 11.1.1...... { 0, 1, 3, 5 } [ . 2 3 4 ] 7: 1.1.11...... { 0, 2, 4, 5 } [ . 1 2 4 ] 8: 1..111...... { 0, 3, 4, 5 } [ . . 2 4 ] 9: 11..11...... { 0, 1, 4, 5 } [ . 2 2 4 ] 10: 111..1...... { 0, 1, 2, 5 } [ . 2 4 4 ] 11: 1.11..1..... { 0, 2, 3, 6 } [ . 1 3 3 ] 12: 11.1..1..... { 0, 1, 3, 6 } [ . 2 3 3 ] 13: 1.1.1.1..... { 0, 2, 4, 6 } [ . 1 2 3 ] 14: 1..11.1..... { 0, 3, 4, 6 } [ . . 2 3 ] 15: 11..1.1..... { 0, 1, 4, 6 } [ . 2 2 3 ] 16: 1.1..11..... { 0, 2, 5, 6 } [ . 1 1 3 ] 17: 1..1.11..... { 0, 3, 5, 6 } [ . . 1 3 ] 18: 11...11..... { 0, 1, 5, 6 } [ . 2 1 3 ] 19: 111...1..... { 0, 1, 2, 6 } [ . 2 4 3 ] 20: 1.11...1.... { 0, 2, 3, 7 } [ . 1 3 2 ] 21: 11.1...1.... { 0, 1, 3, 7 } [ . 2 3 2 ] 22: 1.1.1..1.... { 0, 2, 4, 7 } [ . 1 2 2 ] 23: 1..11..1.... { 0, 3, 4, 7 } [ . . 2 2 ] 24: 11..1..1.... { 0, 1, 4, 7 } [ . 2 2 2 ] 25: 1.1..1.1.... { 0, 2, 5, 7 } [ . 1 1 2 ] 26: 1..1.1.1.... { 0, 3, 5, 7 } [ . . 1 2 ] 27: 11...1.1.... { 0, 1, 5, 7 } [ . 2 1 2 ] 28: 1.1...11.... { 0, 2, 6, 7 } [ . 1 . 2 ] 29: 1..1..11.... { 0, 3, 6, 7 } [ . . . 2 ] 30: 11....11.... { 0, 1, 6, 7 } [ . 2 . 2 ] 31: 111....1.... { 0, 1, 2, 7 } [ . 2 4 2 ] 32: 1.11....1... { 0, 2, 3, 8 } [ . 1 3 1 ] 33: 11.1....1... { 0, 1, 3, 8 } [ . 2 3 1 ] 34: 1.1.1...1... { 0, 2, 4, 8 } [ . 1 2 1 ] 35: 1..11...1... { 0, 3, 4, 8 } [ . . 2 1 ] 36: 11..1...1... { 0, 1, 4, 8 } [ . 2 2 1 ] 37: 1.1..1..1... { 0, 2, 5, 8 } [ . 1 1 1 ] 38: 1..1.1..1... { 0, 3, 5, 8 } [ . . 1 1 ] 39: 11...1..1... { 0, 1, 5, 8 } [ . 2 1 1 ] 40: 1.1...1.1... { 0, 2, 6, 8 } [ . 1 . 1 ] 41: 1..1..1.1... { 0, 3, 6, 8 } [ . . . 1 ] 42: 11....1.1... { 0, 1, 6, 8 } [ . 2 . 1 ] 43: 111.....1... { 0, 1, 2, 8 } [ . 2 4 1 ] 44: 1.11.....1.. { 0, 2, 3, 9 } [ . 1 3 . ] 45: 11.1.....1.. { 0, 1, 3, 9 } [ . 2 3 . ] 46: 1.1.1....1.. { 0, 2, 4, 9 } [ . 1 2 . ] 47: 1..11....1.. { 0, 3, 4, 9 } [ . . 2 . ] 48: 11..1....1.. { 0, 1, 4, 9 } [ . 2 2 . ] 49: 1.1..1...1.. { 0, 2, 5, 9 } [ . 1 1 . ] 50: 1..1.1...1.. { 0, 3, 5, 9 } [ . . 1 . ] 51: 11...1...1.. { 0, 1, 5, 9 } [ . 2 1 . ] 52: 1.1...1..1.. { 0, 2, 6, 9 } [ . 1 . . ] 53: 1..1..1..1.. { 0, 3, 6, 9 } [ . . . . ] 54: 11....1..1.. { 0, 1, 6, 9 } [ . 2 . . ] 55: 111......1.. { 0, 1, 2, 9 } [ . 2 4 . ] ct=55