27 citations · 83 across the 20 of their papers we have counts for
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Covering by planks and avoiding zeros of polynomials
Alexey Glazyrin, Roman Karasev, Alexandr Polyanskii
We note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex…
A cap covering theorem
Alexandr Polyanskii
A cap of spherical radius on a unit -sphere is the set of points within spherical distance from a given point on the sphere. Let be a finite set of caps…
Perron and Frobenius meet Carathéodory
Márton Naszódi, Alexandr Polyanskii
We present a new approach of proving certain Carathéodory-type theorems using the Perron-Frobenius Theorem, a classical result in matrix theory describing the largest eigenvalue of…
On almost-equidistant sets - II
Alexandr Polyanskii
A set in is called almost-equidistant if for any three distinct points in the set, some two are at unit distance apart. First, we give a short proof of the result of…
On almost-equidistant sets
Alexandr Polyanskii
A finite set of points in is called almost-equidistant if among any three distinct points in the set, some two are at unit distance. We prove that an almost-equidista…
Proof of László Fejes Tóth's zone conjecture
Zilin Jiang, Alexandr Polyanskii
A zone of width on the unit sphere is the set of points within spherical distance of a given great circle. We show that the total width of any collection of zones coverin…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Alexandr Polyanskii +1
We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in -di…
Helly-type theorem for eigenvectors
Alexandr Polyanskii
We prove that if any or fewer elements of a finite family of linear operators ( is an arbitrary field) have a common e…
Pairwise intersecting homothets of a convex body
Alexandr Polyanskii
We show that the maximum number of pairwise intersecting positive homothets of a -dimensional centrally symmetric convex body, none of which contains the center of another in it…
On reduced polytopes
Alexandr Polyanskii
A convex body in is called reduced if the minimal width of each convex body different from is strictly smaller than the minimal width $Δ…
Proof of Schur's conjecture in
Andrey B. Kupavskii, Alexandr Polyanskii
In this paper we prove Schur's conjecture in , which states that any diameter graph in the Euclidean space on vertices may have at most cliqu…