Frankl's union-closed conjecture: Difference between revisions
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Created page with "<h1>Polymath11 -- Frankl's union-closed conjecture</h1> A family <math>\mathcal{A}</math> of sets is called <em>union closed</em> if <math>A\cup B\in\mathcal{A}</math> whenev..." |
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A family <math>\mathcal{A}</math> of sets is called <em>union closed</em> if <math>A\cup B\in\mathcal{A}</math> whenever <math>A\in\mathcal{A}</math> and <math>B\in\mathcal{A}</math>. Frankl's conjecture is a disarmingly simple one: if <math>\mathcal{A}</math> is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people. | A family <math>\mathcal{A}</math> of sets is called <em>union closed</em> if <math>A\cup B\in\mathcal{A}</math> whenever <math>A\in\mathcal{A}</math> and <math>B\in\mathcal{A}</math>. Frankl's conjecture is a disarmingly simple one: if <math>\mathcal{A}</math> is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people. | ||
<h2>Discussion on Gowers's Weblog</h2> | |||
* [https://gowers.wordpress.com/2016/01/21/frankls-union-closed-conjecture-a-possible-polymath-project/ Introductory post] | |||
* [https://gowers.wordpress.com/2016/01/29/func1-strengthenings-variants-potential-counterexamples/ FUNC1] | |||
<h2>Links</h2> | |||
* A good [http://www.zaik.uni-koeln.de/~schaudt/UCSurvey.pdf survey article] | |||
Revision as of 10:05, 30 January 2016
Polymath11 -- Frankl's union-closed conjecture
A family [math]\displaystyle{ \mathcal{A} }[/math] of sets is called union closed if [math]\displaystyle{ A\cup B\in\mathcal{A} }[/math] whenever [math]\displaystyle{ A\in\mathcal{A} }[/math] and [math]\displaystyle{ B\in\mathcal{A} }[/math]. Frankl's conjecture is a disarmingly simple one: if [math]\displaystyle{ \mathcal{A} }[/math] is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people.
Discussion on Gowers's Weblog
Links
- A good survey article
