Titel
The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis
Autor*in
Guy Louchard
Université Libre de Bruxelles
Autor*in
Werner Schachinger
Autor*in
Mark Daniel Ward
Purdue University
Abstract
The analysis of strings of n random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the asymptotic (n→∞) mean of this number in the cases of different and identical pairs. In this paper we are interested in all asymptotic moments in the identical case, in the asymptotic variance in the different case and in the asymptotic distribution in both cases. We use two approaches: the first one, the probabilistic approach, leads to variances in both cases and to some conjectures on all moments in the identical case and on the distribution in both cases. The second approach, the combinatorial one, relies on multivariate pattern matching techniques, yielding exact formulas for first and second moments. We use such tools as Mellin transforms, Analytic Combinatorics, Markov Chains.
Stichwort
MathematicsProbability
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:2064245
Erschienen in
Titel
Discrete Mathematics & Theoretical Computer Science
Band
vol. 25:2
Ausgabe
Combinatorics
ISSN
1365-8050
Erscheinungsdatum
2023
Verlag
Centre pour la Communication Scientifique Directe (CCSD)
Erscheinungsdatum
2023
Zugänglichkeit
Rechteangabe
© 2023 by the author(s)

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