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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2018 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/126128 |
| Online Access: | https://hdl.handle.net/2117/126128 https://dx.doi.org/10.1016/j.laa.2018.10.015 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
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