An Erdős–Ko–Rado Theorem for Direct Products |
| |
Authors: | P. Frankl |
| |
Affiliation: | Université Paris 6, Combinatoire, 4 place Jussieu, Paris, 75005, France |
| |
Abstract: | Letni, kibe positive integers,i=1, ..., d,satisfyingni≥2ki.LetX1, ..., Xdbe pairwise disjoint sets with |Xi| =ni.Letbe the family of those (k1+···+kd)-element sets which have exactlykielements inXi, i=1,..., d.It is shown that if⊂is an intersecting family then ||/||≤maxiki/ni,and this is best possible. The proof is algebraic, although in thed=2 case a combinatorial argument is presented as well. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|