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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)

- Charlotte A. C. Brennan, Arnold Knopfmacher, Stephan G. Wagner
- Combinatorics, Probability & Computing
- 2008

- Charlotte A. C. Brennan
- Ars Comb.
- 2011

- Aubrey Blecher, Charlotte A. C. Brennan, Arnold Knopfmacher
- Discrete Mathematics & Theoretical Computer…
- 2014

- Charlotte A. C. Brennan, Arnold Knopfmacher
- Discrete Mathematics & Theoretical Computer…
- 2009

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)

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 at position i, if ai+1 ≥ ai + d. We study the average position, initial height and end height of the first ascent of size d or more in… (More)

- Margaret Archibald, Aubrey Blecher, Charlotte A. C. Brennan, Arnold Knopfmacher, Toufik Mansour
- Australasian J. Combinatorics
- 2016

In this paper we study the largest parts in integer partitions according to multiplicities and part sizes. Firstly we investigate various properties of the multiplicities of the largest parts. We then consider the sum of the m largest parts first as distinct parts and then including multiplicities. Finally, we find the generating function for the sum of the… (More)

- Charlotte A. C. Brennan
- Discrete Mathematics
- 2007

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)

- Charlotte A. C. Brennan, Simon Mavhungu
- Fundam. Inform.
- 2012