// output of ./demo/comb/composition-nz-stats-demo.cc: // Description: //% Statistics for compositions into non-zero parts. //% Cf. the following OEIS sequences: //% A048004: Compositions by value of largest part. //% A105147: compositions by value of smallest part. //% A119473: compositions by number of even values. //% A100749: compositions by number of odd values. //% A105422: compositions by number of ones //% A106356: compositions by number of flat steps //% A238130: compositions by number of non-flat steps //% A225084: compositions by max ascent arg 1: 6 == n [Compositions of n] default=6 arg 2: 0 == sq [Select stats: 0 ==> by largest part 1 ==> by smallest part 3 ==> by number of largest parts 4 ==> by number of smallest parts 5 ==> by number of ones 10 ==> by number of descents 11 ==> by number of ascents (same as number of descents) 30 ==> number of smallest parts 31 ==> number of largest parts 40 ==> position of first occurrence of largest part 41 ==> position of last occurrence of largest part 42 ==> position of first occurrence of smallest part 43 ==> position of last occurrence of smallest part 50 ==> number of even values 51 ==> number of odd values 60 ==> by number of fixed points (offset 0) 61 ==> by number of fixed points (offset 1) 70 ==> number of flat steps 71 ==> number of non-flat steps 80 ==> max ascent 81 ==> max descent (same as max ascent) ] default=0 1: [ 1 1 1 1 1 1 ] 1 2: [ 1 1 1 1 2 ] 2 3: [ 1 1 1 2 1 ] 2 4: [ 1 1 1 3 ] 3 5: [ 1 1 2 1 1 ] 2 6: [ 1 1 2 2 ] 2 7: [ 1 1 3 1 ] 3 8: [ 1 1 4 ] 4 9: [ 1 2 1 1 1 ] 2 10: [ 1 2 1 2 ] 2 11: [ 1 2 2 1 ] 2 12: [ 1 2 3 ] 3 13: [ 1 3 1 1 ] 3 14: [ 1 3 2 ] 3 15: [ 1 4 1 ] 4 16: [ 1 5 ] 5 17: [ 2 1 1 1 1 ] 2 18: [ 2 1 1 2 ] 2 19: [ 2 1 2 1 ] 2 20: [ 2 1 3 ] 3 21: [ 2 2 1 1 ] 2 22: [ 2 2 2 ] 2 23: [ 2 3 1 ] 3 24: [ 2 4 ] 4 25: [ 3 1 1 1 ] 3 26: [ 3 1 2 ] 3 27: [ 3 2 1 ] 3 28: [ 3 3 ] 3 29: [ 4 1 1 ] 4 30: [ 4 2 ] 4 31: [ 5 1 ] 5 32: [ 6 ] 6 0, 1, 12, 11, 5, 2, 1, ct=32