google-deepmind / google-deepmind/formal-conjectures

Green's Open Problems #70

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green-problems new conjecture
Dominant language
Lean
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Description

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.70

Fix integers $k, l$. Is it true that, given a set of $n \geq n\_0(k, l)$ points in $\mathbb{R}^2$, either some $k$ of them lie on a line, or some $l$ of them are 'mutually visible', that is to say that line segment joining them contains no other point from the set?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-05
* ams-52

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Contributor guide

Open the contributing guide

Research direction

Start with problem 70 in the linked Green's Open Problems PDF, then inspect existing formalized conjectures in the repository to understand the expected Lean structure. Done means adding a formal statement of this conjecture to the collection and ensuring it is accepted by the repository's checks.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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