Sequences by Number of w-Rises
Morton Abramson · Canadian Mathematical Bulletin · 1975
An m-permutation of n, repetitions allowed, is an m-sequence (1) A w-rise is a pair (ei, ei+1) such that ei+1-ei≥w>0. In this note we find an expression for Tk, w(n, m), the number of m-sequences having precisely k w-rises. The case w = 1 is given in [1] [2]. Also, when w = 1 we give the number when each of the integers 1, 2, …, r must appear at least once.