Mason's conjecture on the equivalence of two definitions of symmetric powers of matroids is proven for k=2 and refuted for k≥3.
Rigidity of graphs and frameworks: A matroid theoretic approach
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an isometry of $\mathbb{R}^d$. The study of rigid frameworks has increased rapidly since the 1970s stimulated by numerous applications in areas such as civil and mechanical engineering, CAD, molecular conformation, sensor network localisation and low rank matrix completion. We will describe some of the main results in combinatorial rigidity theory and their applications to other areas of combinatorics, putting an emphasis on links to matroid theory.
fields
math.CO 2years
2026 2representative citing papers
A combinatorial characterization of generic infinitesimal rigidity for frameworks in any Euclidean dimension is given using Plücker relations on the Grassmannian and Young's straightening law on tableaux.
citing papers explorer
-
Symmetric Powers of Matroids
Mason's conjecture on the equivalence of two definitions of symmetric powers of matroids is proven for k=2 and refuted for k≥3.
-
Generic Rigidity of Graph Frameworks in Euclidean Space
A combinatorial characterization of generic infinitesimal rigidity for frameworks in any Euclidean dimension is given using Plücker relations on the Grassmannian and Young's straightening law on tableaux.