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

作　　者：Jiu Qiang LIU Sheng Gui ZHANG Ji Meng XIAO 

机构地区：[1]School of Management Engineering, Xi'an University of Finance and Economics, Xi'an 710100, P. R. China [2]Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA [3]Department of Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第7期1087-1100,共14页数学学报（英文版）

摘　　要：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 E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 （2004）]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.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 E-intersections by Furedi and Sudakov [J. Combin. Theory, Set. A, 105, 143-159 （2004）]. We will also derive similar results on E-intersecting families of subspaces of an n-dimensional vector space over a finite field Fq, where q is a prime power.

关 键 词：Alon-Babai-Suzuki Theorem Erdos-Ko-Rado Theorem Frankl-Wilson Theorem Snevily Theorem multilinear polynomials 

分 类 号：O174.14[理学—数学]