G. Averkov

most citedRepresenting elementary semi-algebraic sets by a few polynomial inequalities: A constructive approach

6 citations · 8 across the 5 of their papers we have counts for

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math.MG2008★ 1 cited

Three-dimensional polyhedra can be described by three polynomial inequalities

Gennadiy Averkov, Martin Henk

Bosse et al. conjectured that for every natural number $d \geq 2$ and every $d$ -dimensional polytope $P$ in $ℜ^{d}$ there exist $d$ polynomials $p_{0} (x), ..., p_{d - 1} (x)$ satisfying…

math.MG2007★ 1 cited

Representing simple d-dimensional polytopes by d polynomials

Gennadiy Averkov, Martin Henk

A polynomial representation of a convex d-polytope P is a finite set \{p_1(x),...,p_n(x)\} of polynomials over E^d such that P=\setcond{x \in \E^d}{p_1(x) \ge 0 {for every} 1 \le i…

math.MG2007

Retrieving convex bodies from restricted covariogram functions

Gennadiy Averkov, Gabriele Bianchi

The covariogram g_K(x) of a convex body K \subseteq E^d is the function which associates to each x \in E^d the volume of the intersection of K with K+x. Matheron asked whether g_K…