The first ascent of size d or more in compositions
نویسندگان
چکیده
Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more at position i if ai+1 ≥ ai + d. In (3) the present authors found the distribution of the number of ascents of size d or more in compositions of n. In this paper we study various statistics relating to the first ascent of size d or more in compositions of n. In particular we find the average initial height, end height and position of the first ascent of size greater than or equal to d.
منابع مشابه
The distribution of ascents of size d or more in compositions
A composition of a positive integer n is a finite sequence of positive integers a1, a2, . . . , ak such that a1 + a2 + · · ·+ ak = n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more if ai+1 ≥ ai +d. We determine the mean, variance and limiting distribution of the number of ascents of size d or more in the set of compositions of n. We also study the average ...
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