Triangular sequences, combinatorial recurrences and linear difference equations

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 rel...

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Detalles Bibliográficos
Autores: Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373, Jiménez Jiménez, María José|||0000-0003-3502-462X
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/126128
Acceso en línea:https://hdl.handle.net/2117/126128
https://dx.doi.org/10.1016/j.laa.2018.10.015
Access Level:acceso abierto
Palabra clave:Combinatorial analysis
Combinatorial identities
Triangular matrices
Linear difference equations
Three-term recurrences
Orthogonal polynomials
Anàlisi combinatòria
Classificació AMS::11 Number theory::11B Sequences and sets
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::05 Combinatorics::05A Enumerative combinatorics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descripción
Sumario: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.