A. Garber

activity

20242026

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5 papers · 1 filter

math.CO2026

Ehrhart Theory over Abelian Group Rings

Robert Davis, JesÃºs 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…

math.CO2025

Flips in Two-dimensional Hypertriangulations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2

We study flips in hypertriangulations of planar points sets. Here a level- $k$ hypertriangulation of $n$ points in the planes is a subdivision induced by the projection of a $k$ -hyp…

math.CO2025

Voronoi conjecture for five-dimensional parallelohedra

Alexey Garber

We prove the Voronoi conjecture for five-dimensional parallelohedra. Namely, we show that if a convex five-dimensional polytope $P$ tiles $R^{5}$ with translations, then $P$ …

math.CO2024

Brillouin Zones of Integer Lattices and Their Perturbations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +3

For a locally finite set, $A \subseteq R^{d}$ , the $k$ -th Brillouin zone of $a \in A$ is the region of points $x \in R^{d}$ for which $∥ x - a ∥$ is the $k$ -th smallest…

math.CO2024

Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem

Esme Bajo, Robert Davis, JesÃºs A. De Loera +4

We generalize R. P. Stanley's celebrated theorem that the $h^{*}$ -polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under contai…