Talk:Happy ending problem

General position[edit]

Brendan: is it really necessary to say no two points coincident, in the general position footnote? I'd think that would be covered by calling them a set. —David Eppstein 16:21, 7 October 2006 (UTC)[reply]

It's not mathematically necessary, and in fact it is also covered by "no three points are collinear". So it can be removed. On the other hand, this article is aimed at general readers, who might find some redundancy helpful. I'm happy either way. McKay 04:41, 15 November 2006 (UTC)[reply]

Name[edit]

Why is it named the 'happy ending' problem? Thanks! - Fasrad 04:03, 15 November 2006 (UTC)[reply]

See the first sentence of the article. McKay 04:36, 15 November 2006 (UTC)[reply]

Thanks! I need to stop reading Wikipedia late at night. Fasrad 19:57, 19 January 2007 (UTC)[reply]

But how exactly did its solution lead to a marriage? --Gwern (contribs) 19:48 7 January 2011 (GMT)

My recollection is that the HEP is the general statement, that is, for every n there is an f(n) such that it is true that among f(n) points some n form a convex polygon (and not the special case f(4)=5 proved by Ms Klein). Kope 16:24, 16 June 2007 (UTC)[reply]

Another reference[edit]

In hopes of convincing Tompw (talk · contribs) that the importance is more than low, here's an application of closely related ideas to an important open problem in algorithms: arXiv:cs/0610092. But I'm not going to do more than mention this here for fear of violating WP:OR. —David Eppstein 19:10, 4 January 2007 (UTC)[reply]

Updated citation: Eppstein, D. (2007). "Happy endings for flip graphs". 23rd Annual Symposium on Computational Geometry, Gyeongju, South Korea. pp. 92–101. arXiv:cs/0610092. doi:10.1145/1247069.1247084. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help) So no longer any danger of being original research, but I'll let someone else mention it in the article here or not as they see fit as I think adding it myself would be too much of a conflict of interest. I've added self-refs to other articles, but only when they're more central to the topic; this one isn't so much about the happy ending problem itself as an application of related ideas to a different problem. It does, though, include a more efficient new algorithm for finding empty pentagons when they exist. —David Eppstein 16:58, 16 June 2007 (UTC)[reply]

Erdős–Szekeres conjecture... theorem![edit]

I have proven the Erdős–Szekeres conjecture. The solution to it can be found on my website... http://www.oddperfectnumbers.com. It maps distinctly to the coverings of the posts on a Towers of Hanoi. I'm not trying to break any guidelines, just trying to provide the only answer; (talk) 22:27, 20 October 2012 (UTC)[reply]

The next step is to get it reliably published. We can't really do anything here unless/until that happens. —David Eppstein (talk) 05:02, 21 October 2012 (UTC)[reply]

In m-dimension[edit]

If k points must in a form of n-point m-dimension convex polygon, then $k=m^{n-m}+1$ — Preceding unsigned comment added by 115.80.80.42 (talk) 13:57, 26 June 2014 (UTC)[reply]

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