11 citations · 47 across the 48 of their papers we have counts for
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math.MG2007★ 1 cited
Confirmation of Matheron's conjecture on the covariogram of a planar convex body
Gennadiy Averkov, Gabriele Bianchi
The covariogram g_K of a convex body K in E^d is the function which associates to each x in E^d the volume of the intersection of K with K+x. In 1986 G. Matheron conjectured that f…
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…