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  On the distribution of the number of missing words in Random texts

Rahmann, S. (2003). On the distribution of the number of missing words in Random texts. Combinatorics, Probability and Computing, 12(1), 72-87. doi:10.1017/S0963548302005473.

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 Creators:
Rahmann, Sven1, Author           
Affiliations:
1Dept. of Computational Molecular Biology (Head: Martin Vingron), Max Planck Institute for Molecular Genetics, Max Planck Society, ou_1433547              

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 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 [sigma] 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[minus sign]1 over the given alphabet? For q=1, X is the number Y of empty urns with [sigma] urns and n balls. For q[gt-or-equal, slanted]2, X is related to the number Y of empty urns with [sigma]q 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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Language(s): eng - English
 Dates: 2003-01
 Publication Status: Issued
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 Rev. Type: -
 Identifiers: eDoc: 176099
DOI: 10.1017/S0963548302005473
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Title: Combinatorics, Probability and Computing
Source Genre: Journal
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Pages: - Volume / Issue: 12 (1) Sequence Number: - Start / End Page: 72 - 87 Identifier: ISSN: 0963-5483
ISSN: 1469-2163