Let [n] denote the set {1, 2, ..., n}, 2([n]) the collection of all subsets of [n] and F subset of 2([n]) be a family. The maximum of F is studied if any r subsets have an at least s-element intersection and there are no l subsets containing t + 1 common elements. We show that F less than or equal to Sigma(i=0)(t-s) ((n-s)(i)) + (t+l-s)/(t+2-s) ((n-s)(t+1-s)) + l - 2 and this bound is asymptotically the best possible as n --> infinity and t greater than or equal to 2s greater than or equal to 2, r, lgreater than or equal to2 are fixed. (C) 2004 Published by Elsevier Inc.
展开▼
机译：令[n]表示集合{1、2，...，n}，2（[n]）的集合，其中[n]的所有子集和2（[n]）的F子集是一个族。如果任何r个子集具有至少s个元素的交集并且不存在包含t +1个公共元素的l个子集，则研究 F 的最大值。我们证明 F 小于或等于Sigma（i = 0）（ts）（（ns）（i））+（t + ls）/（t + 2-s）（（ns）（t + 1 -s））+ l-2，并且此边界渐近地最好，因为n->无穷大，并且t大于或等于2s大于或等于2，r，lgreater大于或等于2是固定的。 （C）2004由Elsevier Inc.出版
展开▼
