OpenAlex ·
A counterexample to Gale's conjecture in $\mathbb{R}^3$
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2610.28828
- Original
- Read it at the publisher
- Topics
Abstract
It is known that for every partition of the sphere $S^2$ of unit diameter into four parts, the largest diameter of a part is at least $\sqrt{(3+\sqrt{3})/6} = 0.88807\dots$, and this bound is attained. The conjecture of D.~Gale (1953) asserts that no set in $\mathbb{R}^3$ has a larger ratio. In this paper, we construct a $101$-point set $V\subset\mathbb{R}^3$ such that every partition of $V$ into four parts contains a part of diameter greater than $0.88928 \, \operatorname{diam} V$.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Graphics
An Exact 93-Move Solution to a Nonlocal Crystal-Exchange Puzzle
A simplified proof of the FPRAS for counting perfect matchings
Temporal Exploration and Rendezvous via Weisfeiler-Leman Colorings
Recent progress in the construction of Hadamard matrices
Polynomial pathwidth for graphs vertex-coverable by few shortest paths and algorithms for quasi-shortest path covers
Get the few papers worth your time in Graphics every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.