Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization
Combinatorics
2022-05-16 v3 Metric Geometry
Abstract
We showed in the first paper of this series that the generic -cofactor matroid is the unique maximal abstract -rigidity matroid. In this paper we obtain a combinatorial characterization of independence in this matroid. This solves the cofactor counterpart of the combinatorial characterization problem for the rigidity of generic 3-dimensional bar-joint frameworks. We use our characterization to verify that the counterparts of conjectures of Dress (on the rank function) and Lov\'{a}sz and Yemini (which suggested a sufficient connectivity condition for rigidity) hold for this matroid.
Keywords
Cite
@article{arxiv.1911.00207,
title = {Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization},
author = {Katie Clinch and Bill Jackson and Shin-ichi Tanigawa},
journal= {arXiv preprint arXiv:1911.00207},
year = {2022}
}