// output of ./demo/comb/partition-nonsquashing-desc-demo.cc: // Description: //% Non-squashing partitions as weakly descending list of parts. //% A non-squashing partition of n is a partition a[1] + a[2] + ... + a[m] = n //% such that a[k] >= sum(j=k+1..m, a[j] ). //% Lexicographic order. //% With parameter sd = true generate strongly decreasing partitions: //% partitions such that a[k] > sum(j=k+1..m, a[j] ). //% See: //% N. J. A. Sloane, James A. Sellers: "On Non-Squashing Partitions", //% arXiv:math/0312418 [math.CO], (22-December-2003). //% Cf. OEIS sequences A018819, A000123 (non-squashing), and A040039 (strongly decreasing). arg 1: 20 == n [non-squashing (or strongly decreasing) partitions of n] default=20 arg 2: 0 == sd [whether strongly decreasing (otherwise non-squashing)] default=0 1: [ 5] [ 10 5 3 1 1 ] 2: [ 4] [ 10 5 3 2 ] 3: [ 4] [ 10 5 4 1 ] 4: [ 3] [ 10 5 5 ] 5: [ 5] [ 10 6 2 1 1 ] 6: [ 4] [ 10 6 2 2 ] 7: [ 4] [ 10 6 3 1 ] 8: [ 3] [ 10 6 4 ] 9: [ 4] [ 10 7 2 1 ] 10: [ 3] [ 10 7 3 ] 11: [ 4] [ 10 8 1 1 ] 12: [ 3] [ 10 8 2 ] 13: [ 3] [ 10 9 1 ] 14: [ 2] [ 10 10 ] 15: [ 5] [ 11 5 2 1 1 ] 16: [ 4] [ 11 5 2 2 ] 17: [ 4] [ 11 5 3 1 ] 18: [ 3] [ 11 5 4 ] 19: [ 4] [ 11 6 2 1 ] 20: [ 3] [ 11 6 3 ] 21: [ 4] [ 11 7 1 1 ] 22: [ 3] [ 11 7 2 ] 23: [ 3] [ 11 8 1 ] 24: [ 2] [ 11 9 ] 25: [ 5] [ 12 4 2 1 1 ] 26: [ 4] [ 12 4 2 2 ] 27: [ 4] [ 12 4 3 1 ] 28: [ 3] [ 12 4 4 ] 29: [ 4] [ 12 5 2 1 ] 30: [ 3] [ 12 5 3 ] 31: [ 4] [ 12 6 1 1 ] 32: [ 3] [ 12 6 2 ] 33: [ 3] [ 12 7 1 ] 34: [ 2] [ 12 8 ] 35: [ 4] [ 13 4 2 1 ] 36: [ 3] [ 13 4 3 ] 37: [ 4] [ 13 5 1 1 ] 38: [ 3] [ 13 5 2 ] 39: [ 3] [ 13 6 1 ] 40: [ 2] [ 13 7 ] 41: [ 4] [ 14 3 2 1 ] 42: [ 3] [ 14 3 3 ] 43: [ 4] [ 14 4 1 1 ] 44: [ 3] [ 14 4 2 ] 45: [ 3] [ 14 5 1 ] 46: [ 2] [ 14 6 ] 47: [ 4] [ 15 3 1 1 ] 48: [ 3] [ 15 3 2 ] 49: [ 3] [ 15 4 1 ] 50: [ 2] [ 15 5 ] 51: [ 4] [ 16 2 1 1 ] 52: [ 3] [ 16 2 2 ] 53: [ 3] [ 16 3 1 ] 54: [ 2] [ 16 4 ] 55: [ 3] [ 17 2 1 ] 56: [ 2] [ 17 3 ] 57: [ 3] [ 18 1 1 ] 58: [ 2] [ 18 2 ] 59: [ 2] [ 19 1 ] 60: [ 1] [ 20 ] ct=60