4 papers
Ehrhart Theory over Abelian Group Rings
Robert Davis, Jesús A. De Loera, Alexey Garber +3
We introduce a unified framework for Ehrhart theory in which lattice point enumerators take coefficients in an Abelian group ring, encoding substantially richer algebraic data than…
On the Ehrhart Theory of Generalized Symmetric Edge Polytopes
Robert Davis, Akihiro Higashitani, Hidefumi Ohsugi
The symmetric edge polytope (SEP) of a (finite, undirected) graph is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. SEPs have been stu…
A Note on Conjectures of Gullerud, Johnson, and Mbirika
Robert Davis, Nayda Farnsworth
In 2023, Gullerud, Johnson, and Mbirika presented results on their study of certain tridiagonal real symmetric matrices. As part of their work, they studied the roots to nonhomogen…
Flow polytopes for extensions of bipartite graphs
Benjamin Braun, Kaitlin Bruegge, Robert Davis +1
The space of unit flows on a finite acyclic directed graph is a lattice polytope called the flow polytope of the graph. Given a bipartite graph with minimum degree at least two…