Combinatorial recurrences and linear difference equations

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related with the solution of l...

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Detalles Bibliográficos
Autores: Jiménez Jiménez, María José|||0000-0003-3502-462X, Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Tipo de recurso: artículo
Fecha de publicación:2016
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:2117/90923
Acceso en línea:https://hdl.handle.net/2117/90923
https://dx.doi.org/10.1016/j.endm.2016.09.054
Access Level:acceso abierto
Palabra clave:Difference equations
Matrices
Orthogonal polynomials
Combinatorial identities
Triangular matrices
Finite difference equations
Equacions en diferències
Matrius (Matemàtica)
Polinomis ortogonals
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::11 Number theory::11C Polynomials and matrices
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
Descripción
Sumario:In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related with the solution of linear three–terms recurrences. We show through some simple examples how this triangular arrays appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers