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arXiv · 2501.03302

A class of inequalities for intersection-closed set systems

Rainer Schrader
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Abstract

Let $N$ be a finite set and $\mathcal{F}$, an intersection-closed family of subsets. Frankl conjectured that there always exists an element in $N$ which is contained in at most half the number of sets in $\mathcal{F}$ unless $\mathcal{F} =\{E\}$. We prove the validity of a class of inequalities which imply Frankl's conjecture.

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Rainer Schrader. 2025-01-06. A class of inequalities for intersection-closed set systems. https://arxiv.org/abs/2501.03302

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