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...
| Autores: | , |
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| 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 |
| 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. |
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