11 citations · 22 across the 12 of their papers we have counts for
5 papers · 1 filter
An algebraic proof of 1-extension
Alexander Heaton, Martin Winter
We give a new proof that 1-extension preserves generic local rigidity of bar-joint frameworks in all dimensions. The proof does not use a special position argument, which makes the…
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…
Facet volumes of polytopes
Pavle V. M. Blagojević, Paul Breiding, Alexander Heaton
In this paper, motivated by the work of Edelman and Strang, we show that for fixed integers and the configuration space of all facet volume vectors of all …
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…
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…