On Symmetric Intersecting Families
نویسندگان
چکیده
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 family has size at most exp ( − c(n− 2k) log n k(log n− log k) )( n k ) , where c > 0 is a universal constant. We also describe various combinatorial and algebraic approaches to constructing such families.
منابع مشابه
Intersecting Families in the Alternating Group and Direct Product of Symmetric Groups
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تاریخ انتشار 2017