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The distribution of ascents of size d or more in samples of geometric random variables We consider words or strings of characters a1a2a3. .. an of length n, where the letters ai ∈ N are independently generated with a geometric probability P{X = k} = pq k−1 where p + q = 1. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more… (More)

A composition of a positive integer n is a finite sequence of positive integers a1, a2,. .. , a k such that a1 + a2 + · · · + a k = 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… (More)

In this paper, compositions of n are studied. These are sequences of positive integers (σ i) k i=1 whose sum is n. We define a maximum to be a part which is greater than or equal to all other parts. We investigate the size of the descents immediately following any maximum and we focus particularly on the largest and average of these, obtaining the… (More)

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)

Compositions are conceptualized as non alternating sequences of blocks of non-decreasing and strictly decreasing partitions. We find the generating function F (x, y, q) where x marks the size of the composition, y the number of parts and q the number of such partition blocks minus 1. We form these blocks starting on the left-hand-side of the composition and… (More)