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Constructing pathological symmetric abstract rigidity matroids
Abstract
We prove that for each d ≥ 2, there exist infinitely many symmetric abstract d-rigidity matroids that are not the d-rigidity matroid, the d-hyperconnectivity matroid, or the d-cofactor matroid. When d=2, our constructed matroids are pathological, in the sense that they are not contained within any abstract 2-rigidity matroid family. Our construction additionally provides a counter-example to a conjecture of Tyomkyn.
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BibTeX
@misc{dewar2026constructing,
title = {{Constructing pathological symmetric abstract rigidity matroids}},
author = {Sean Dewar and Joannes Vermant},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12036},
eprint = {2610.12036},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12036},
}
RIS
TY - UNPB
TI - Constructing pathological symmetric abstract rigidity matroids
AU - Sean Dewar
AU - Joannes Vermant
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12036
UR - https://arxiv.org/abs/2610.12036
AB - We prove that for each d ≥ 2, there exist infinitely many symmetric abstract d-rigidity matroids that are not the d-rigidity matroid, the d-hyperconnectivity matroid, or the d-cofactor matroid. When d=2, our constructed matroids are pathological, in the sense that they are not contained within any abstract 2-rigidity matroid family. Our construction additionally provides a counter-example to a conjecture of Tyomkyn.
ER -