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...
| Autores: | , |
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| 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 |
| 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 |
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