Computation of k-ary Lyndon words using generating functions and their differential equations

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dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2021-02-19T21:16:40Z
dc.date.available2021-02-19T21:16:40Z
dc.date.issued2018
dc.departmentALKÜ
dc.descriptionKUCUKOGLU, IREM/0000-0001-9100-2252
dc.description.abstractBy using generating functions technique, we investigate some properties of the k-ary Lyndon words. We give an explicit formula for the generating functions including not only combinatorial sums, but also hypergeometric function. We also derive higher-order differential equations and some formulas related to the k-ary Lyndon words. By applying these equations and formulas, we also derive some novel identities including the Stirling numbers of the second kind, the Apostol-Bernoulli numbers and combinatorial sums. Moreover, in order to compute numerical values of the higher-order derivative for the generating functions enumerating k-ary Lyndon words with prime number length, we construct an efficient algorithm. By applying this algorithm, we give some numerical values for these derivative equations for selected different prime numbers.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz UniversityAkdeniz University [FDK-2017-2375]
dc.description.sponsorshipThe present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FDK-2017-2375).
dc.identifier.doi10.2298/FIL1810455K
dc.identifier.endpage3463en_US
dc.identifier.issn0354-5180
dc.identifier.issue10en_US
dc.identifier.scopusqualityQ3
dc.identifier.startpage3455en_US
dc.identifier.urihttps://doi.org/10.2298/FIL1810455K
dc.identifier.urihttps://hdl.handle.net/20.500.12868/511
dc.identifier.volume32en_US
dc.identifier.wosWOS:000461181400006
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthor0-belirlenecek
dc.language.isoen
dc.publisherUniv Nis, Fac Sci Math
dc.relation.ispartofFilomat
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectLyndon words
dc.subjectGenerating functions
dc.subjectOrdinary differential equations
dc.subjectApostol-Bernoulli numbers and polynomials
dc.subjectStirling numbers
dc.subjectAlgorithm
dc.titleComputation of k-ary Lyndon words using generating functions and their differential equations
dc.typeArticle

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