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

Jiu Qiang Liu, Sheng Gui Zhang, Ji Meng Xiao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we provide a common generalization to the well-known Erdös–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 Füredi and Sudakov [J. Combin. Theory, Ser. A, 105, 143–159 (2004)]. We will also derive similar results on L-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.

Original languageEnglish
Pages (from-to)1087-1100
Number of pages14
JournalActa Mathematica Sinica, English Series
Volume34
Issue number7
DOIs
StatePublished - 1 Jul 2018

Keywords

  • 05D05
  • Alon–Babai–Suzuki Theorem
  • Erdös–Ko–Rado Theorem
  • Frankl–Wilson Theorem
  • multilinear polynomials
  • Snevily Theorem

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