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arXiv · 2609.33187

A product inequality and its application to cross-intersecting families

Toshihiro Shimizu·Norihide Tokushige
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Abstract

For an integer $r\geq 3$ and real numbers $a_1,\ldots,a_r\in(0,1)$, let $a=a_1\cdots a_r$. We show that \[ \prod_{i=1}^r(a_i+a_i^2+\cdots+a_i^r)\geq \prod_{i=1}^r(a_i+a_i^2+\cdots+a_i^{r-1}+a). \] This inequality enables us to bound the measure of $r$-cross $t$-intersecting families.

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Toshihiro Shimizu, Norihide Tokushige. 2026-09-27. A product inequality and its application to cross-intersecting families. https://arxiv.org/abs/2609.33187

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