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

作者：Liu, Jiu Qiang^*; Zhang, Sheng Gui; Xiao, Ji Meng

来源：Acta Mathematica Sinica-English Series, 2018, 34(7): 1087-1100.

DOI：10.1007/s10114-018-6577-0

• Alon-Babai-Suzuki Theorem
• Erdos-Ko-Rado Theorem
• Frankl-Wilson Theorem
• Snevily Theorem
• multilinear polynomials

In this paper, we provide a common generalization to the well-known Erdos-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, 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 F-q , where q is a prime power.

• 出版日期2018-7
• 单位西北工业大学; 西安财经大学