A. Garber

activity

20242026

collaborators

4 papers

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.DS2024

Substitution tilings with transcendental inflation factor

Dirk FrettlÃ¶h, Alexey Garber, Neil MaÃ±ibo

For any $I^» > 2$ , we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $I^»$ . In particular, we obtain the first class o…