Difference between revisions of "Frankl's union-closed conjecture"

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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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Revision as of 03:01, 27 January 2016

Polymath11 -- Frankl's union-closed conjecture

A family [math]\mathcal{A}[/math] of sets is called union closed 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.