11 citations · 47 across the 48 of their papers we have counts for
13 papers · 1 filter
On the Log-submodularity for zonoids: from Mixed Volume inequalities to the Hypercube
Gennadiy Averkov, Katherina von Dichter, Ivan Soprunov
We prove a log-submodularity-type inequality for zonoids in , extending the three-dimensional result of Fradelizi, Madiman, Meyer, and Zvavitch. More generally, we co…
Exact Flatness Constant for One-Point Convex Bodies and the Discrete Isominwidth Problem: The Planar Case
Gennadiy Averkov, Giulia Codenotti, Ansgar Freyer +1
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in with at most interior lattice points. The maximum…
Inequalities between mixed volumes of convex bodies: volume bounds for the Minkowski sum
Gennadiy Averkov, Christopher Borger, Ivan Soprunov
In the course of classifying generic sparse polynomial systems which are solvable in radicals, Esterov recently showed that the volume of the Minkowski sum of -d…
Homometry and direct-sum decompositions of lattice-convex sets
Gennadiy Averkov, Barbara Langfeld
Two sets in are called homometric if they have the same covariogram, where the covariogram of a finite subset of is the function associating to ea…
Covariograms generated by valuations
Gennadiy Averkov, Gabriele Bianchi
Let ϕbe a real-valued valuation on the family of compact convex subsets of \mathbb{R}^n and let K be a convex body in \mathbb{R}^n. We introduce the ϕ-covariogram g_{K,ϕ} of K as t…
On the size of lattice simplices with a single interior lattice point
Gennadiy Averkov
Let be the set of all -dimensional simplices in with integer vertices and a single integer point in the interior of . It follows from a resul…