Borsuk's problem, Boltyanski's illumination problem, and circumradius

DOI10.2140/moscow.2023.12.223OpenAlexW4386988836MaRDI QIDQ6055511

Arthur Bikeev

Publication date: 29 September 2023

Published in: Moscow Journal of Combinatorics and Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/moscow.2023.12.223

zbMATH Keywords

illuminationcombinatorial geometrycircumradiuscircumcenterconstant widthillumination numberBorsuk's problemBoltyanski's illumination problemcovering of body by its positive homothetic copies

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Illuminating and covering convex bodies
• Measures of symmetry for convex sets and stability
• Zerlegung ebener Bereiche in konvexe Zellen von möglichst kleinem Durchmesser
• Covering a plane convex body by its negative homothets
• Combinatorial problems on the illumination of convex bodies
• The geometry of homothetic covering and illumination
• Partition of three-dimensional sets into five parts of smaller diameter
• Partition bounded sets into sets having smaller diameters
• Borsuk's partition conjecture
• Coverings of planar and three-dimensional sets with subsets of smaller diameter
• On Borsuk's conjecture for two-distance sets
• Sets of constant width in finite dimensional Banach spaces
• Coloring Distance Graphs and Graphs of Diameters
• A counterexample to Borsuk’s conjecture
• Illuminating sets of constant width
• Covering convex bodies by translates of convex bodies
• On a bound in Borsuk's problem
• HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL
• Covering a sphere with spheres
• Covering planar sets
• Covering planar sets
• Covering a convex body by its negative homothetic copies.