G. Averkov

activity

20072026

most citedClassification of triples of lattice polytopes with a given mixed volume

11 citations · 47 across the 48 of their papers we have counts for

collaborators

Showing 2011Show all

5 papers · 1 filter

math.OC2011★ 1 cited

A proof of Lovász's theorem on maximal lattice-free sets

Gennadiy Averkov

Let $K$ be a maximal lattice-free set in $R^{d}$ , that is, $K$ is convex and closed subset of $R^{d}$ , the interior of $K$ does not cointain points of $Z^{d}$ …

math.OC2011

On finitely generated closures in the theory of cutting planes

Gennadiy Averkov

Let $P$ be a rational polyhedron in $R^{d}$ and let $L$ be a class of $d$ -dimensional maximal lattice-free rational polyhedra in $R^{d}$ . For $L \in \mathca…

math.OC2011

On maximal S-free sets and the Helly number for the family of S-convex sets

Gennadiy Averkov

We study two combinatorial parameters, which we denote by f(S) and h(S), associated to an arbitrary set S \subseteq R^d, where d \in N. In the nondegenerate situation, f(S) is the…

math.OC2011★ 4 cited

On finite generation and infinite convergence of generalized closures from the theory of cutting planes

Gennadiy Averkov

For convex sets $K$ and $L$ in $R^{d}$ we define $R_{L} (K)$ to be the convex hull of all points belonging to $K$ but not to the interior of $L$ . Cutting-plane methods from i…

math.MG2011★ 1 cited

On the size of lattice simplices with a single interior lattice point

Gennadiy Averkov

Let $T^{d} (1)$ be the set of all $d$ -dimensional simplices $T$ in $ℜ^{d}$ with integer vertices and a single integer point in the interior of $T$ . It follows from a resul…