Bill Jackson

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20242026

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5 papers · 1 filter

math.CO2025

Sufficient conditions for bipartite rigidity, symmetric completability and hyperconnectivity of graphs

Dániel Garamvölgyi, Bill Jackson, Tibor Jordán +1

We consider three matroids defined by Kalai in 1985: the symmetric completion matroid $S_{d}$ on the edge set of a looped complete graph; the hyperconnectivity matroid $\ma…

math.CO2025

Sparsity, Stress-Independence and Globally Linked Pairs in Graph Rigidity Theory

Dániel Garamvölgyi, Bill Jackson, Tibor Jordán

A graph is $R_{d}$ -independent (resp. $R_{d}$ -connected) if its $d$ -dimensional generic rigidity matroid is free (resp. connected). A result of Maxwell from 1867 im…

math.HO2025

Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach

James Cruickshank, Bill Jackson, Tibor Jordán +1

A $d$ -dimensional (bar-and-joint) framework $(G, p)$ consists of a graph $G = (V, E)$ and a realisation $p : V \to R^{d}$ . It is rigid if every continuous motion of the vertices wh…

math.CO2025

Symmetric Tensor Matroids, Dual Rigidity Matroids, and the Maximality Conjecture

Bill Jackson, Shin-ichi Tanigawa

Inspired by a recent result of Brakensiek et al. that symmetric tensor matroids and rigidity matroids are linked by matroid duality, we define abstract symmetric tensor matroids as…

math.CO2025

Volume Rigidity of Simplicial Manifolds

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

Classical results of Cauchy and Dehn imply that the 1-skeleton of a convex simplicial polyhedron $P$ is rigid i.e. every continuous motion of the vertices of $P$ in $R^{3}$ w…