منابع مشابه
Families intersecting on an interval
We shall be interested in the following Erdős-Ko-Rado-type question. Fix some set B ⊂ [n]. How large a family A ⊂ P [n] can we find such that the intersection of any two sets in A contains a cyclic translate (modulo n) of B? Chung, Graham, Frankl and Shearer have proved that, in the case where B is a block of length t, we can do no better than to take A to consist of all supersets of B. We give...
متن کاملOn Symmetric Intersecting Families
A family of sets is said to be symmetric if its automorphism group is transitive, and intersecting if any two sets in the family have nonempty intersection. Our purpose here is to study the following question: for n, k ∈ N with k ≤ n/2, how large can a symmetric intersecting family of k-element subsets of {1, 2, . . . , n} be? As a first step towards a complete answer, we prove that such a fami...
متن کاملOn cross-intersecting families
Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says ...
متن کاملOn Shadows Of Intersecting Families
The shadow minimization problem for t-intersecting systems of finite sets is considered. Let A be a family of k-subsets of N. The -shadow of A is the set of all (k− )-subsets ∂ A contained in the members of A. Let A be a t-intersecting family (any two members have at least t elements in common) with |A| =m. Given k,t,m the problem is to minimize |∂ A| (over all choices of A). In this paper we s...
متن کاملChain Intersecting Families
Let F be a family of subsets of an n-element set. F is called (p,q)-chain intersecting if it does not contain chains A1 ( A2 ( · · · ( Ap and B1 ( B2 ( · · · ( Bq with Ap∩Bq = ∅. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.07.008