Bivariate generating functions for a class of linear recurrences: General structure

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Show simple item record Barbero G., J. Fernando Salas Martínez, Jesús Sánchez Villaseñor, Eduardo Jesús 2017-05-22T10:33:27Z 2017-05-22T10:33:27Z 2014-07
dc.identifier.bibliographicCitation Journal of Combinatorial Theory, Series A, 2014, 125, pp. 146-165.
dc.identifier.issn 0097-3165
dc.description.abstract We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many cases of combinatorial interest for particular choices of the six parameters that define it. We give a complete classification of the partial differential equations satisfied by the exponential generating functions, and solve them in all cases. We also show that the recurrence relations defining the combinatorial numbers appearing in this problem display an interesting degeneracy that we study in detail. Finally, we obtain for all cases the corresponding univariate row generating polynomials.
dc.description.sponsorship We are indebted to Alan Sokal for his participation in the early stages of this work, and his encouragement and useful suggestions later on. We also thank Jesper Jacobsen, Anna de Mier, Neil Sloane, and Mike Spivey for correspondence, and David Callan for pointing out some interesting references to us. This research has been supported in part by Spanish MINECO grant FIS2012-34379. The research of J.S. has also been supported in part by Spanish MINECO grant MTM2011-24097 and by U.S. National Science Foundation grant PHY-0424082.
dc.format.extent 20
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2014 Elsevier
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Recurrence equations
dc.subject.other Exponential generating functions
dc.subject.other Row generating polynomials
dc.title Bivariate generating functions for a class of linear recurrences: General structure
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. FIS2012-34379
dc.relation.projectID Gobierno de España. MTM2011-24097
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 146
dc.identifier.publicationlastpage 165
dc.identifier.publicationtitle Journal of Combinatorial Theory. Series A
dc.identifier.publicationvolume 125
dc.identifier.uxxi AR/0000015196
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