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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Detalles Bibliográficos
Autor: Esteban Pascual, Guillermo
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
Descripción
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.