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White's Conjecture for Paving Matroids
Yu-Chuan Yu, Chi Ho Yuen
White's conjecture asserts that any two tuples of matroid bases that have the same multi-set union can be transformed from one to another by symmetric exchanges; it also implies th…
Filtrations of Tope Spaces of Oriented Matroids
Kris Shaw, Chi Ho Yuen
We compare three filtrations of the tope space of an oriented matroid. The first is the dual Varchenko-Gelfand degree filtration, the second filtration is from Kalinin's spectral s…
A Consistent Sandpile Torsor Algorithm for Regular Matroids
Changxin Ding, Alex McDonough, Lilla Tóthmérész +1
Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion o…
Eigenvalues and Critical Groups of Adinkras
Kevin Iga, Caroline Klivans, Jordan Kostiuk +1
Adinkras are signed graphs used to study supersymmetry in physics. We provide an introduction to these objects, and study the properties of their signed adjacency and signed Laplac…
Patchworking Oriented Matroids
Marcel Celaya, Georg Loho, Chi Ho Yuen
In a previous work, we gave a construction of (not necessarily realizable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a v…
Oriented Matroids from Triangulations of Products of Simplices
Marcel Celaya, Georg Loho, Chi Ho Yuen
We introduce a construction of oriented matroids from a triangulation of a product of two simplices. For this, we use the structure of such a triangulation in terms of polyhedral m…