A Common Generalization to Theorems on Set Systems with L-intersections

2017/07/06 by Jiuqiang Liu, Liu, Jiuqiang, Shenggui Zhang +3
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1707.01715

openalex publication_date 2017/07/06 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28

Abstract

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

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