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{\bf Ivica Bo\v snjak and Petar Markovi\'c}
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{\bf The $11$-element case of Frankl's conjecture}
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In 1979, P.~Frankl conjectured that in a finite union-closed
family ${\cal F}$ of finite sets, ${\cal
F}\neq\{\emptyset\}$, there has to be an element that belongs to at
least half of the sets in ${\cal F}$. We prove this when
$|\bigcup{\cal F}|\leq 11$.



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