New production matrices for geometric graphs
We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another, simple and elegant, way of counting the number of such objects. Counting geometric graphs i...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2022 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/360864 |
| Acesso em linha: | https://hdl.handle.net/2117/360864 https://dx.doi.org/10.1016/j.laa.2021.10.013 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Graph theory Generating functions Riordan Arrays Production matrices Characteristic polynomials Geometric graphs Anàlisi combinatòria Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
| Resumo: | We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another, simple and elegant, way of counting the number of such objects. Counting geometric graphs is then equivalent to calculating the powers of a production matrix. Applying the technique of Riordan Arrays to these production matrices, we establish new formulas for the numbers of geometric graphs as well as combinatorial identities derived from the production matrices. Further, we obtain the characteristic polynomial and the eigenvectors of such production matrices. |
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