Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Shimizu, Toshihiro, Tokushige, Norihide
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214742796