23 citations · 112 across the 26 of their papers we have counts for
28 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…
Bounds for the Regularity Radius of Delone Sets
Nikolay Dolbilin, Alexey Garber, Egon Schulte +1
Delone sets are discrete point sets in characterized by parameters , where (usually) is the smallest inter-point distance of , and is the radi…
Weighted Ehrhart Theory: Extending Stanley's nonnegativity theorem
Esme Bajo, Robert Davis, Jesús A. De Loera +4
We generalize R. P. Stanley's celebrated theorem that the -polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under contai…
Flips in Two-dimensional Hypertriangulations
Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari +2
We study flips in hypertriangulations of planar points sets. Here a level- hypertriangulation of points in the planes is a subdivision induced by the projection of a -hyp…
Catalan numbers as discrepancies for a family of substitutions on infinite alphabets
Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. Wh…
Substitution tilings with transcendental inflation factor
Dirk Frettlöh, Alexey Garber, Neil Mañibo
For any , we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor . In particular, we obtain the first class of…