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On the Distribution of the Number of Missing Words in Random Texts

Sven Rahmann 1 Eric Rivals 2
2 MAB - Méthodes et Algorithmes pour la Bioinformatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Determining the distribution of the number of empty urns after a number of balls have been thrown randomly into the urns is a classical and well understood problem. We study a generalization: Given a finite alphabet of size σ and a word length q, what is the distribution of the number X of words (of length q) that do not occur in a random text of length n+q−1 over the given alphabet? For q=1, X is the number Y of empty urns with σ urns and n balls. For q[gt-or-equal, slanted]2, X is related to the number Y of empty urns with σq urns and n balls, but the law of X is more complicated because successive words in the text overlap. We show that, perhaps surprisingly, the laws of X and Y are not as different as one might expect, but some problems remain currently open.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00269581
Contributor : Christine Carvalho de Matos <>
Submitted on : Thursday, April 3, 2008 - 8:21:53 AM
Last modification on : Friday, August 31, 2018 - 9:26:03 AM

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Sven Rahmann, Eric Rivals. On the Distribution of the Number of Missing Words in Random Texts. Combinatorics, Probability and Computing, Cambridge University Press (CUP), 2003, 12 (1), pp.73-87. ⟨10.1017/S0963548302005473⟩. ⟨lirmm-00269581⟩

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