Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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DMTCS vol 5 no 1 (2002), pp. 71-96

Discrete Mathematics & Theoretical Computer Science


Volume 5 n° 1 (2002), pp. 71-96

author:Guy Louchard and Helmut Prodinger
title:Probabilistic Analysis of Carlitz Compositions
keywords:Carlitz compositions, Smirnov words, polyominoes, central limit theorems, local limit theorems, large deviation theorems, Markov chains, Brownian motion
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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reference: Guy Louchard and Helmut Prodinger (2002), Probabilistic Analysis of Carlitz Compositions, Discrete Mathematics and Theoretical Computer Science 5, pp. 71-96
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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