New results on production matrices for geometric graphs

We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of n points i...

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Detalhes bibliográficos
Autores: Esteban Pascual, Guillermo, Huemer, Clemens|||0000-0001-7557-0823, Silveira, Rodrigo Ignacio|||0000-0003-0202-4543
Formato: artículo
Fecha de publicación:2018
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/121756
Acesso em linha:https://hdl.handle.net/2117/121756
https://dx.doi.org/10.1016/j.endm.2018.06.037
Access Level:acceso abierto
Palavra-chave:Combinatorial analysis
geometric graph
production matrix
Riordan array
Anàlisi combinatòria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
Descrição
Resumo:We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of n points in convex position in the plane, is presented. Further, we find the characteristic polynomials and we provide a characterization of the eigenvectors of the production matrices.