Borsuk's partition conjecture

DOI10.1007/s11537-021-2007-7zbMath1484.52013OpenAlexW3183651628WikidataQ113900229 ScholiaQ113900229MaRDI QIDQ2067690

Chuan Ming Zong

Publication date: 18 January 2022

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-021-2007-7

zbMATH Keywords

partitiondiameterlattice polytopesBorsuk's problem

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Combinatorial complexity of geometric structures (52C45)

Related Items

Borsuk's partition problem in ℓₚ⁴, Coverings of planar and three-dimensional sets with subsets of smaller diameter, Borsuk's problem, Boltyanski's illumination problem, and circumradius, Complete sets in normed linear spaces, Banach-Mazur distance from \(\ell_p^3\) to \(\ell_\infty^3\), On Boltyanski and Gohberg's partition conjecture

Cites Work

• A 64-dimensional counterexample to Borsuk's conjecture
• A quantitative program for Hadwiger's covering conjecture
• Intersection theorems with geometric consequences
• An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
• New sets with large Borsuk numbers
• Some remarks concerning kissing numbers, blocking numbers and covering numbers
• On Borsuk's conjecture for two-distance sets
• On the number of convex lattice polytopes
• Ein geometrisches Überdeckungsproblem
• Überdeckung einer Menge durch Mengen kleineren Durchmessers
• Mitteilung betreffend meine Note: Überdeckung einer Menge durch Mengen kleineren Durchmessers
• Zur Zerlegung von Punktmengen in solche kleineren Durchmessers
• On the classification of convex lattice polytopes
• A counterexample to Borsuk’s conjecture
• Zum Borsukschen Zerteilungsproblem
• On the blocking number and the covering number of a convex body
• Illuminating sets of constant width
• Über Durchschnittseigenschaften n-dimensionaler Kugelfamilien.
• Bodies of Constant Width
• Solution of Hadwiger's Covering Problem for Centrally Symmetric Convex Bodies in E ³
• Symmetrical sets of constant width and their partitions
• On Inscribing n-Dimensional Sets in a Regular n-Simplex
• Covering a Three-Dimensional set with Sets of Smaller Diameter
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item