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math.CO2026
Generic Rigidity and the Grassmannian
Alexander Heaton
We characterize the generic rigidity of bar-joint frameworks in all dimensions. The conditions are constructed explicitly from the graph alone, independently of any placement, and…
math.CO2020★ 5 cited
Dual matroid polytopes and internal activity of independence complexes
Alexander Heaton, Jose Alejandro Samper
Shelling orders are a ubiquitous tool used to understand invariants of cell complexes. Significant effort has been made to develop techniques to decide when a given complex is shel…
math.CO2019
An SOS counterexample to an inequality of symmetric functions
Alexander Heaton, Isabelle Shankar
It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparab…