TY - JOUR
T1 - A Common Generalization to Theorems on Set Systems with L-intersections
AU - Liu, Jiu Qiang
AU - Zhang, Sheng Gui
AU - Xiao, Ji Meng
N1 - Publisher Copyright:
© 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - 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.
AB - 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.
KW - 05D05
KW - Alon–Babai–Suzuki Theorem
KW - Erdös–Ko–Rado Theorem
KW - Frankl–Wilson Theorem
KW - multilinear polynomials
KW - Snevily Theorem
UR - http://www.scopus.com/inward/record.url?scp=85040914508&partnerID=8YFLogxK
U2 - 10.1007/s10114-018-6577-0
DO - 10.1007/s10114-018-6577-0
M3 - 文章
AN - SCOPUS:85040914508
SN - 1439-8516
VL - 34
SP - 1087
EP - 1100
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 7
ER -