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A product inequality and its application to cross-intersecting families
Abstract
For an integer r≥ 3 and real numbers a1,…,ar∈(0,1), let a=a1⋯ ar. We show that ∏i=1r(ai+ai2+⋯+air)≥ ∏i=1r(ai+ai2+⋯+air−1+a). This inequality enables us to bound the measure of r-cross t-intersecting families.
Related
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BibTeX
@misc{shimizu2026product,
title = {{A product inequality and its application to cross-intersecting families}},
author = {Toshihiro Shimizu and Norihide Tokushige},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33187},
eprint = {2609.33187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33187},
}
RIS
TY - UNPB
TI - A product inequality and its application to cross-intersecting families
AU - Toshihiro Shimizu
AU - Norihide Tokushige
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33187
UR - https://arxiv.org/abs/2609.33187
AB - For an integer r≥ 3 and real numbers a_1,…,a_r∈(0,1), let a=a_1⋯ a_r. We show that ∏_i=1^r(a_i+a_i^2+⋯+a_i^r)≥ ∏_i=1^r(a_i+a_i^2+⋯+a_i^r−1+a). This inequality enables us to bound the measure of r-cross t-intersecting families.
ER -