// output of ./demo/comb/young-tab-rgs-demo.cc: // Description: //% Restricted growth strings (RGS) for standard Young tableaux: //% the k-th occurrence of a digit d in the RGS must precede //% the k-th occurrence of the digit d+1. //% Lexicographic order. //% The strings are also called ballot sequences. //% Cf. OEIS sequences A000085 (all tableaux), //% A001405 (tableaux with height <= 2, central binomial coefficients) //% A001006 (tableaux with height <= 3, Motzkin numbers) //% A005817 (height <= 4), A049401 (height <= 5), A007579 (height <= 6) //% A007578 (height <= 7), A007580 (height <= 8), A212915 (height <= 9), //% A212916 (height <= 10). //% A001189 (height <= n-1), //% A014495 (height = 2), A217323 (height = 3), A217324 (height = 4), //% A217325 (height = 5), A217326 (height = 6), A217327 (height = 7), //% A217328 (height = 8). //% Cf. A182172 (tableaux of n cells and height <= k). //% Cf. OEIS sequences A061343 (all shifted tableaux; using condition is_shifted(1)), //% A210736 (shifted, height <= 2), A082395 (shifted, height <= 3). //% Cf. OEIS sequences A161125 (descent numbers), A225617 (strict inversions), //% and A225618 (weak inversions). arg 1: 6 == n [Length of strings] default=6 arg 2: 0 == m [Number of allowed values for digits == max height of tableaux, 0 ==> all] default=0 arg 3: 0 == tq [Whether do draw tableaux (as ASCII art)] default=0 1: [ . . . . . . ] 0 [ 6 . . . . . ] 1 2: [ . . . . . 1 ] 5 [ 5 1 . . . . ] 2 3: [ . . . . 1 . ] 4 [ 5 1 . . . . ] 2 4: [ . . . . 1 1 ] 5 [ 4 2 . . . . ] 2 5: [ . . . . 1 2 ] 5 [ 4 1 1 . . . ] 3 6: [ . . . 1 . . ] 3 [ 5 1 . . . . ] 2 7: [ . . . 1 . 1 ] 5 [ 4 2 . . . . ] 2 8: [ . . . 1 . 2 ] 5 [ 4 1 1 . . . ] 3 9: [ . . . 1 1 . ] 4 [ 4 2 . . . . ] 2 10: [ . . . 1 1 1 ] 5 [ 3 3 . . . . ] 2 11: [ . . . 1 1 2 ] 5 [ 3 2 1 . . . ] 3 12: [ . . . 1 2 . ] 4 [ 4 1 1 . . . ] 3 13: [ . . . 1 2 1 ] 5 [ 3 2 1 . . . ] 3 14: [ . . . 1 2 3 ] 5 [ 3 1 1 1 . . ] 4 15: [ . . 1 . . . ] 2 [ 5 1 . . . . ] 2 16: [ . . 1 . . 1 ] 5 [ 4 2 . . . . ] 2 17: [ . . 1 . . 2 ] 5 [ 4 1 1 . . . ] 3 18: [ . . 1 . 1 . ] 4 [ 4 2 . . . . ] 2 19: [ . . 1 . 1 1 ] 5 [ 3 3 . . . . ] 2 20: [ . . 1 . 1 2 ] 5 [ 3 2 1 . . . ] 3 21: [ . . 1 . 2 . ] 4 [ 4 1 1 . . . ] 3 22: [ . . 1 . 2 1 ] 5 [ 3 2 1 . . . ] 3 23: [ . . 1 . 2 3 ] 5 [ 3 1 1 1 . . ] 4 24: [ . . 1 1 . . ] 3 [ 4 2 . . . . ] 2 25: [ . . 1 1 . 1 ] 5 [ 3 3 . . . . ] 2 26: [ . . 1 1 . 2 ] 5 [ 3 2 1 . . . ] 3 27: [ . . 1 1 2 . ] 4 [ 3 2 1 . . . ] 3 28: [ . . 1 1 2 2 ] 5 [ 2 2 2 . . . ] 3 29: [ . . 1 1 2 3 ] 5 [ 2 2 1 1 . . ] 4 30: [ . . 1 2 . . ] 3 [ 4 1 1 . . . ] 3 31: [ . . 1 2 . 1 ] 5 [ 3 2 1 . . . ] 3 32: [ . . 1 2 . 3 ] 5 [ 3 1 1 1 . . ] 4 33: [ . . 1 2 1 . ] 4 [ 3 2 1 . . . ] 3 34: [ . . 1 2 1 2 ] 5 [ 2 2 2 . . . ] 3 35: [ . . 1 2 1 3 ] 5 [ 2 2 1 1 . . ] 4 36: [ . . 1 2 3 . ] 4 [ 3 1 1 1 . . ] 4 37: [ . . 1 2 3 1 ] 5 [ 2 2 1 1 . . ] 4 38: [ . . 1 2 3 4 ] 5 [ 2 1 1 1 1 . ] 5 39: [ . 1 . . . . ] 1 [ 5 1 . . . . ] 2 40: [ . 1 . . . 1 ] 5 [ 4 2 . . . . ] 2 41: [ . 1 . . . 2 ] 5 [ 4 1 1 . . . ] 3 42: [ . 1 . . 1 . ] 4 [ 4 2 . . . . ] 2 43: [ . 1 . . 1 1 ] 5 [ 3 3 . . . . ] 2 44: [ . 1 . . 1 2 ] 5 [ 3 2 1 . . . ] 3 45: [ . 1 . . 2 . ] 4 [ 4 1 1 . . . ] 3 46: [ . 1 . . 2 1 ] 5 [ 3 2 1 . . . ] 3 47: [ . 1 . . 2 3 ] 5 [ 3 1 1 1 . . ] 4 48: [ . 1 . 1 . . ] 3 [ 4 2 . . . . ] 2 49: [ . 1 . 1 . 1 ] 5 [ 3 3 . . . . ] 2 50: [ . 1 . 1 . 2 ] 5 [ 3 2 1 . . . ] 3 51: [ . 1 . 1 2 . ] 4 [ 3 2 1 . . . ] 3 52: [ . 1 . 1 2 2 ] 5 [ 2 2 2 . . . ] 3 53: [ . 1 . 1 2 3 ] 5 [ 2 2 1 1 . . ] 4 54: [ . 1 . 2 . . ] 3 [ 4 1 1 . . . ] 3 55: [ . 1 . 2 . 1 ] 5 [ 3 2 1 . . . ] 3 56: [ . 1 . 2 . 3 ] 5 [ 3 1 1 1 . . ] 4 57: [ . 1 . 2 1 . ] 4 [ 3 2 1 . . . ] 3 58: [ . 1 . 2 1 2 ] 5 [ 2 2 2 . . . ] 3 59: [ . 1 . 2 1 3 ] 5 [ 2 2 1 1 . . ] 4 60: [ . 1 . 2 3 . ] 4 [ 3 1 1 1 . . ] 4 61: [ . 1 . 2 3 1 ] 5 [ 2 2 1 1 . . ] 4 62: [ . 1 . 2 3 4 ] 5 [ 2 1 1 1 1 . ] 5 63: [ . 1 2 . . . ] 2 [ 4 1 1 . . . ] 3 64: [ . 1 2 . . 1 ] 5 [ 3 2 1 . . . ] 3 65: [ . 1 2 . . 3 ] 5 [ 3 1 1 1 . . ] 4 66: [ . 1 2 . 1 . ] 4 [ 3 2 1 . . . ] 3 67: [ . 1 2 . 1 2 ] 5 [ 2 2 2 . . . ] 3 68: [ . 1 2 . 1 3 ] 5 [ 2 2 1 1 . . ] 4 69: [ . 1 2 . 3 . ] 4 [ 3 1 1 1 . . ] 4 70: [ . 1 2 . 3 1 ] 5 [ 2 2 1 1 . . ] 4 71: [ . 1 2 . 3 4 ] 5 [ 2 1 1 1 1 . ] 5 72: [ . 1 2 3 . . ] 3 [ 3 1 1 1 . . ] 4 73: [ . 1 2 3 . 1 ] 5 [ 2 2 1 1 . . ] 4 74: [ . 1 2 3 . 4 ] 5 [ 2 1 1 1 1 . ] 5 75: [ . 1 2 3 4 . ] 4 [ 2 1 1 1 1 . ] 5 76: [ . 1 2 3 4 5 ] 5 [ 1 1 1 1 1 1 ] 6 ct=76