Cross-intersection theorems for uniform partitions of finite sets

Tian Yao; Mengyu Cao; Haixiang Zhang

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arXiv · 2509.17188

Cross-intersection theorems for uniform partitions of finite sets

Tian Yao·Mengyu Cao·Haixiang Zhang

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Abstract

A set partition is $c$-uniform if every block has size $c$. Two families of $c$-uniform partitions of a finite set are said to be cross $t$-intersecting if two partitions from different families share at least $t$ blocks. In this paper, we establish some product-type extremal results for such cross $t$-intersecting families. Our results yield an Erd\H{o}s-Ko-Rado theorem and a Hilton-Milner theorem for uniform set partitions. Additionally, cross $t$-intersecting families with the maximum sum of their sizes are also characterized.

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BibTeX RIS

Tian Yao, Mengyu Cao, Haixiang Zhang. 2025-09-21. Cross-intersection theorems for uniform partitions of finite sets. https://arxiv.org/abs/2509.17188

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