Production matrices and enumeration of geometric graphs
We propose the study of counting problems for geometric graphs defined on point sets in convex position. Many formulae are known, for instance the numbers of triangulations are given by the Catalan numbers. Our approach to that topic is based on generating trees, production matrices, and Riordan arr...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2018 |
| 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:2117/119372 |
| Acceso en línea: | https://hdl.handle.net/2117/119372 |
| Access Level: | acceso abierto |
| Palabra clave: | Combinatorial analysis Geometric graph Production matrix Riordan array Combinacions (Matemàtica) Classificació AMS::05 Combinatorics::05A Enumerative combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria |
| Sumario: | We propose the study of counting problems for geometric graphs defined on point sets in convex position. Many formulae are known, for instance the numbers of triangulations are given by the Catalan numbers. Our approach to that topic is based on generating trees, production matrices, and Riordan arrays. We aim to derive such formulae with the mentioned tools, and also to prove new formulae for the numbers of geometric graphs, as well as relations among them. |
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