矩曲线上的杆-关节刚性与圆锥曲线上的余因子刚性一致
组合数学
2023-03-16 v2
摘要
我们证明，对于矩曲线上的点，杆-关节刚性拟阵与超连通拟阵一致，且二者均与平面上任意（非退化）圆锥曲线上点的 -余因子刚性一致。对于二维超连通性，将点置于矩曲线上并不失一般性。我们还证明，限制在二部图上时，杆-关节刚性拟阵比超连通拟阵更自由。
引用
@article{arxiv.2106.08923,
title = {Bar-and-joint rigidity on the moment curve coincides with cofactor rigidity on a conic},
author = {Luis Crespo Ruiz and Francisco Santos},
journal= {arXiv preprint arXiv:2106.08923},
year = {2023}
}
备注
15 pages. Added details and some additional results, including suggestions from referees. This version has been accepted in "Combinatorial Theory"