منابع مشابه
On 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 Symmetric 3-wise Intersecting Families
A family of sets is said to be symmetric if its automorphism group is transitive, and 3-wise intersecting if any three sets in the family have nonempty intersection. Frankl conjectured in 1981 that if A is a symmetric 3-wise intersecting family of subsets of {1, 2, . . . , n}, then |A| = o(2). Here, we give a short proof of Frankl’s conjecture using a sharp threshold result of Friedgut and Kalai.
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 کاملFamilies 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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2020
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2020.103094