Work

Constructing pathological symmetric abstract rigidity matroids

Year: 2026

Type: preprint

Abstract: We prove that for each $d \geq 2$, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12036

Authors: Dewar, Sean, Vermant, Joannes

Institutions: KU Leuven, Umeå University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, KU Leuven

Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, G4869584417, G4872507874, G562246749, Matroids in Applied and Combinatorial Commutative Algebra, G7618753153

OpenAlex ID: W7221195682

Cites: 15

Cited by:

Related to: 10