Regular intersecting families
نویسندگان
چکیده
منابع مشابه
Regular Intersecting Families
We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families F of k-element subsets of [n] := {1, . . . , n}, such that every element of [n] lies in the same (or approximately the same) number of members of F . In particular, we show that we can guarantee |F| = o( ( n−1 k−1 ) ) if and only if k = o(n).
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Intersection problems occupy an important place in the theory of finite sets. One of the central notions is that of a r-wise r-intersecting family, that is, a collection holds for all choices of 1 < il < < i, < m. What is the maximal size m = m(n, r, t) of a r-wise t-intersecting family? Taking all subsets containing a fixed t-element set shows that m(n, r, 1) > 2 "-' holds for all n 3 f 2 0. O...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2019.07.009