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 to the solution of lin...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics Vol. 54; pp. 313 - 318
Main Authors: Jiménez, M. José, Encinas, Andrés M.
Format: Journal Article Publication
Language:English
Published: Elsevier B.V 01.10.2016
Subjects:
11 Number theory
11C Polynomials and matrices
39 Difference and functional equations
39A Difference equations
Classificació AMS
Combinatorial identities
Difference equations
Equacions diferencials i integrals
Equacions en diferències
Finite difference equations
Matemàtiques i estadística
Matrices
Matrius (Matemàtica)
Orthogonal polynomials
Polinomis ortogonals
Triangular matrices
Àrees temàtiques de la UPC
Combinatorial identities
triangular matrices
finite difference equations
orthogonal polynomials
ISSN:1571-0653, 1571-0653
Online Access:Get full text
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Summary: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 to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appear as essential components in the expression of some classical orthogonal polynomials and combinatorial numbers.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2016.09.054