Difference between revisions of "Main Page"

From Polymath1Wiki
Jump to: navigation, search
Line 1: Line 1:
<big>Polymath1 Wiki</big>
+
== The Problem ==
  
<math>E = mc^2</math>
+
Let <math>[3]^n</math> be the set of all length <math>n</math> strings over the alphabet <math>1, 2, 3</math>.   A ''combinatorial line'' is a set of three points in <math>[3]^n</math>, formed by taking a string with one or more wildcards in it, e.g., <math>112*1**3\ldots</math>, and replacing those wildcards by <math>1, 2</math> and <math>3</math>, respectively.  In the example given, the resulting combinatorial line is:
Consult the [http://meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software.
+
$$
 +
\{ 11211113\ldots, 11221223\ldots, 11231333\ldots \}
 +
$$
 +
The Density Hales-Jewett theorem asserts that for any $\delta > 0$,
 +
for sufficiently large $n = n(\delta)$, all subsets of $[3]^n$ of size
 +
at least $\delta 3^n$ contain a combinatorial line,
  
== Getting started ==
+
== Other resources ==
* [http://www.mediawiki.org/wiki/Manual:Configuration_settings Configuration settings list]
+
 
* [http://www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
+
* [http://blogsearch.google.com/blogsearch?hl=en&ie=UTF-8&q=polymath1&btnG=Search+Blogs Blog posts related to the Polymath1 project]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]
+
* [http://meta.wikimedia.org/wiki/Help:Contents Wiki user's guide]

Revision as of 16:40, 8 February 2009

The Problem

Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards in it, e.g., [math]112*1**3\ldots[/math], and replacing those wildcards by [math]1, 2[/math] and [math]3[/math], respectively. In the example given, the resulting combinatorial line is: $$ \{ 11211113\ldots, 11221223\ldots, 11231333\ldots \} $$ The Density Hales-Jewett theorem asserts that for any $\delta > 0$, for sufficiently large $n = n(\delta)$, all subsets of $[3]^n$ of size at least $\delta 3^n$ contain a combinatorial line,

Other resources