10 citations · 48 across the 37 of their papers we have counts for
43 papers
Symmetric Powers of Matroids
Bill Jackson, Shin-ichi Tanigawa
The study of matroid products has become an active area of research, owing to their connections with tropical ideals and linear representability. In this paper, we study matroidal…
Characterizing globally linked pairs in graphs
Tibor Jordán, Shin-ichi Tanigawa
A pair of vertices is said to be globally linked in a -dimensional framework if there exists no other framework with the same edge lengths, in which th…
Uniquely realizable crystalline structures
Sean Dewar, Bernd Schulze, Shin-ichi Tanigawa +1
We construct infinite periodic versions of the stress matrix and establish sufficient conditions for periodic tensegrity frameworks to be globally rigid in in the ca…
Dilworth truncations and Hadamard products of linear spaces
Dario Antolini, Sean Dewar, Shin-ichi Tanigawa
As a direct application of Dilworth truncations of polymatroids, we give short proofs of two theorems: Bernstein's characterisation of algebraic matroids coming from the Hadamard p…
Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach
James Cruickshank, Bill Jackson, Tibor Jordán +1
A -dimensional (bar-and-joint) framework consists of a graph and a realisation . It is rigid if every continuous motion of the vertices wh…
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…