Triangular sequences, combinatorial recurrences and linear difference equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2019 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 576, pages 301-323 (issn: 0024-3795,

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Authors: Encinas Bachiller, Andrés Marcos; Jiménez Jiménez, María José;

doi: 10.1016/j.laa.2018.10.015

handle: 2117/126128

Triangular sequences, combinatorial recurrences and linear difference equations

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Abstract

In this work we introduce the triangular double sequences of arbitrary order given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular sequences generated by two double sequences and establish their relation with the solution of linear three-term recurrences. We show through some simple examples how these triangular sequences appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers. Peer Reviewed

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Keywords

Combinatorial analysis, Classificació AMS::05 Combinatorics::05A Enumerative combinatorics, Orthogonal polynomials, Classificació AMS::11 Number theory::11B Sequences and sets, Classificació AMS::39 Difference and functional equations::39A Difference equations, :Matemàtiques i estadística::Matemàtica discreta::Combinatòria [Àrees temàtiques de la UPC], Triangular matrices, three-term recurrences, Recurrences, triangular matrices, :11 Number theory::11B Sequences and sets [Classificació AMS], orthogonal polynomials, Combinatorial identities, bijective combinatorics, linear difference equations, Linear difference equations, Combinatorial identities, Bell and Stirling numbers, :39 Difference and functional equations::39A Difference equations [Classificació AMS], combinatorial identities, Binomial coefficients; factorials; \(q\)-identities, Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria, :05 Combinatorics::05A Enumerative combinatorics [Classificació AMS], Three-term recurrences, Factorials, binomial coefficients, combinatorial functions, Anàlisi combinatòria

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