The number of distinct adjacent pairs in geometrically distributed words

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dc.contributor.authorArchibald, Margareten_ZA
dc.contributor.authorBlecher, Aubreyen_ZA
dc.contributor.authorBrennan, Charlotteen_ZA
dc.contributor.authorKnopfmacher, Arnolden_ZA
dc.contributor.authorWagner, Stephanen_ZA
dc.contributor.authorWard, Mark Danielen_ZA
dc.date.accessioned2022-07-01T11:40:04Z
dc.date.available2022-07-01T11:40:04Z
dc.date.issued2021-01-28
dc.descriptionCITATION: Archibald, M. et al. 2021. The number of distinct adjacent pairs in geometrically distributed words. Discrete Mathematics & Theoretical Computer Science, 22(4) doi:10.23638/DMTCS-22-4-10en_ZA
dc.descriptionThe original publication is available at https://dmtcs.episciences.org/en_ZA
dc.description.abstractA sequence of geometric random variables of length n is a sequence of n independent and identically distributed geometric random variables (Γ1,Γ2,…,Γn) where P(Γj=i)=pqi−1 for 1 ≤ j ≤ n with p+q=1. We study the number of distinct adjacent two letter patterns in such sequences. Initially we directly count the number of distinct pairs in words of short length. Because of the rapid growth of the number of word patterns we change our approach to this problem by obtaining an expression for the expected number of distinct pairs in words of length n. We also obtain the asymptotics for the expected number as n→∞.en_ZA
dc.description.urihttps://dmtcs.episciences.org/7121
dc.description.versionPublishers versionen_ZA
dc.format.extent18 pages : illustrationsen_ZA
dc.identifier.citationArchibald, M. et al. 2021. The number of distinct adjacent pairs in geometrically distributed words. Discrete Mathematics & Theoretical Computer Science, 22(4) doi:10.23638/DMTCS-22-4-10en_ZA
dc.identifier.issn1365-8050 (online)
dc.identifier.issn1462-7264 (print)
dc.identifier.otherdoi:10.23638/DMTCS-22-4-10
dc.identifier.urihttp://hdl.handle.net/10019.1/125446
dc.language.isoen_ZAen_ZA
dc.publisherEpisciences.orgen_ZA
dc.rights.holderAuthors retain copyrighten_ZA
dc.subjectGeometric random variablesen_ZA
dc.subjectPairsen_ZA
dc.subjectGenerating functionsen_ZA
dc.subjectAsymptoticsen_ZA
dc.subjectBinary system (Mathematics)en_ZA
dc.titleThe number of distinct adjacent pairs in geometrically distributed wordsen_ZA
dc.typeArticleen_ZA
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