# 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.If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

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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Automatically produced on Wed Apr 24 22:46:15 CEST 2002 by ifalk