google-deepmind / google-deepmind/formal-conjectures

Erdős Problem 174

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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/174

A finite set $A\subset \mathbb{R}^n$ is called Ramsey if, for any $k\geq 1$, there exists some $d=d(A,k)$ such that in any $k$-colouring of $\mathbb{R}^d$ there exists a monochromatic copy of $A$. Characterise the Ramsey sets in $\mathbb{R}^n$.

Status: open

### Prerequisites needed
Not quite so clear what "Characerise" means here, perhaps it might be useful to formalize this using the `answer(sorry)` mechanism, possibly both as sufficient and necessary condition separately.

### 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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