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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2008

Constructions for Clumps Statistics.

Abstract

We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This object has first been studied by Schbath with the aim of counting the number of occurrences of words in random texts. Later work with similar probabilistic approach used the Chen-Stein approximation for a compound Poisson distribution, where the number of clumps follows a law close to Poisson. Presently there is no combinatorial counterpart to this approach, and we fill the gap here. We also provide a construction for the yet unsolved problem of clumps of an arbitrary finite set of words. In contrast with the probabilistic approach which only provides asymptotic results, the combinatorial method provides exact results that are useful when considering short sequences.
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Dates and versions

hal-00452701 , version 1 (02-02-2010)
hal-00452701 , version 2 (09-09-2015)

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Attribution - NonCommercial

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Frédérique Bassino, Julien Clément, Julien Fayolle, Pierre Nicodème. Constructions for Clumps Statistics.. 5th International Colloquium on Mathematics and Computer Science (MathInfo'08), Sep 2008, Blaubeuren, Germany. pp.183-198., ⟨10.46298/dmtcs.3563⟩. ⟨hal-00452701v2⟩
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