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arXiv · 1707.01715

A Common Generalization to Theorems on Set Systems with $\mathcal{L}$-intersections

Jiuqiang Liu·Shenggui Zhang·Jimeng Xiao
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Abstract

In this paper, we provide a common generalization to the well-known Erd\H{o}s-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with $\mathcal{L}$-intersections. As a consequence, we derive a result which strengthens substantially the well-known theorem on set systems with $k$-wise $\mathcal{L}$-intersections by F$\ddot{u}$redi and Sudakov [J. Combin. Theory, Ser. A (2004) 105: 143-159]. We will also derive similar results on $\mathcal{L}$-intersecting families of subspaces of an $n$-dimensional vector space over a finite field $\mathbb{F}_{q}$, where $q$ is a prime power.

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Jiuqiang Liu, Shenggui Zhang, Jimeng Xiao. 2017-07-06. A Common Generalization to Theorems on Set Systems with $\mathcal{L}$-intersections. https://arxiv.org/abs/1707.01715

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