Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic

We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the -cofactor rigidity of points along any (non-degenerate) conic in the plane. For hyperconnectivity in dimension two, having the points in the...

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Detalhes bibliográficos
Autores: Crespo Ruiz, Luis, Santos, Francisco|||0000-0003-2120-9068
Tipo de documento: artigo
Data de publicação:2023
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/31632
Acesso em linha:https://hdl.handle.net/10902/31632
Access Level:Acceso aberto
Palavra-chave:Rigidity
Hyperconnectivity
Moment curve
Cofactor rigidity
Descrição
Resumo:We show that, for points along the moment curve, the bar-and-joint rigidity matroid and the hyperconnectivity matroid coincide, and that both coincide with the -cofactor rigidity of points along any (non-degenerate) conic in the plane. For hyperconnectivity in dimension two, having the points in the moment curve is no loss of generality. We also show that, restricted to bipartite graphs, the bar-and-joint rigidity matroid is freer than the hyperconnectivity matroid.