k-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-lerch zeta function and Apostol-bernoulli polynomials

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dc.authoridKucukoglu, Irem/0000-0001-9100-2252
dc.authoridSIMSEK, YILMAZ/0000-0002-0611-7141
dc.authoridBAYAD, Abdelmejid/0000-0002-8003-335X
dc.authorwosidBAYAD, Abdelmejid/AES-7308-2022
dc.authorwosidKucukoglu, Irem/L-9198-2018
dc.authorwosidSIMSEK, YILMAZ/C-1654-2016
dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorBayad, Abdelmejid
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2024-08-20T20:29:20Z
dc.date.available2024-08-20T20:29:20Z
dc.date.issued2017
dc.departmentAntalya Belek Üniversitesien_US
dc.description.abstractThe main motivation of this paper was to give finite and infinite generating functions for the numbers of the k-ary Lyndon words and necklaces. In order to construct our new generating functions, we use two different methods. The first method is related to the derivative operator t d/dt and the Stirling numbers of the second kind. On the other hand, the second method is related to the Hurwitz-Lerch zeta function and the Apostol-Bernoulli numbers. Moreover, by using these generating functions, we give some applications for some selected numerical values including different prime numbers factorization, the Stirling numbers and also the Bernoulli numbers and polynomials.en_US
dc.description.sponsorshipScientific Research Project Administration of Akdeniz University [FDK-2017-2375]en_US
dc.description.sponsorshipThe present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FDK-2017-2375). We would like to thank the referees for their valuable comments and suggestions on the present paper.en_US
dc.identifier.doi10.1007/s00009-017-1025-4
dc.identifier.issn1660-5446
dc.identifier.issn1660-5454
dc.identifier.issue6en_US
dc.identifier.scopus2-s2.0-85049178605en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1007/s00009-017-1025-4
dc.identifier.urihttps://hdl.handle.net/20.500.14591/100
dc.identifier.volume14en_US
dc.identifier.wosWOS:000414094100007en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSPRINGER BASEL AGen_US
dc.relation.ispartofMediterranean Journal Of Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectLyndon wordsen_US
dc.subjectNecklacesen_US
dc.subjectGenerating functionen_US
dc.subjectSpecial numbers and polynomialsen_US
dc.subjectBernoulli numbers and polynomialsen_US
dc.subjectApostol-Bernoulli numbers and polynomialsen_US
dc.subjectStirling numbers of the second kinden_US
dc.subjectArithmetical functionen_US
dc.subjectHurwitz-Lerch zeta functionen_US
dc.titlek-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-lerch zeta function and Apostol-bernoulli polynomialsen_US
dc.typeArticleen_US

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