6 citations · 8 across the 5 of their papers we have counts for
5 papers
Three-dimensional polyhedra can be described by three polynomial inequalities
Gennadiy Averkov, Martin Henk
Bosse et al. conjectured that for every natural number and every -dimensional polytope in there exist polynomials satisfying…
Notes on algebra and geometry of polynomial representations
Gennadiy Averkov
Consider a semi-algebraic set A in R^d constructed from the sets which are determined by inequalities p_i(x)>0, p_i(x)\ge 0, or p_i(x)=0 for a given list of polynomials p_1,...,p_m…
Representing elementary semi-algebraic sets by a few polynomial inequalities: A constructive approach
Gennadiy Averkov
Let P be an elementary closed semi-algebraic set in R^d, i.e., there exist real polynomials p_1,...,p_s such that P= \{x \in R^d : p_1(x) \ge 0, >..., p_s(x) \ge 0 \}; in this case…
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…
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…