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Sequences by Number of w-Rises
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1975
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