google-deepmind / google-deepmind/formal-conjectures
Erdős Problem 103: diameter minimising incongruent sets
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ams-52: Convex and discrete geometry
erdos-problems
new conjecture
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Description
### What is the conjecture
https://www.erdosproblems.com/103
Let $h(n)$ count the number of incongruent sets of $n$ points in $\mathbb{R}^2$ which minimise the diameter subject to the constraint that $d(x,y)\geq 1$ for all points $x\neq y$. Is it true that $h(n)\to \infty$?
Status: open
### Prerequisites needed
`Congruent` exists, and we should have `diameter` soon, see #330.
### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else
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Assessment
This issue has not been assessed yet.