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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2002

Probabilistic Analysis of Carlitz Compositions

Abstract

Using generating functions and limit theorems, we obtain a stochastic description of Carlitz compositions of large integer n (i.e. compositions two successive parts of which are different). We analyze: the number M of parts, the number of compositions T(m,n) with m parts, the distribution of the last part size, the correlation between two successive parts, leading to a Markov chain. We describe also the associated processes and the limiting trajectories, the width and thickness of a composition. We finally present a typical simulation. The limiting processes are characterized by Brownian Motion and some discrete distributions.

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Dates and versions

hal-00958973 , version 1 (13-03-2014)

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Guy Louchard, Helmut Prodinger. Probabilistic Analysis of Carlitz Compositions. Discrete Mathematics and Theoretical Computer Science, 2002, Vol. 5, pp.71-96. ⟨10.46298/dmtcs.302⟩. ⟨hal-00958973⟩

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