The Intersection Structure of t-Intersecting Families
نویسنده
چکیده
A family of sets is t-intersecting if any two sets from the family contain at least t common elements. Given a t-intersecting family of r-sets from an n-set, how many distinct sets of size k can occur as pairwise intersections of its members? We prove an asymptotic upper bound on this number that can always be achieved. This result can be seen as a generalization of the Erdős-Ko-Rado theorem.
منابع مشابه
A new approach for assessing stability of rock slopes considering centroids of weak zones
The intersection lines between discontinuity surfaces and their intersection points on the visible surfaces of any engineering structure may be the instability indicators. This paper describes a new approach to modelling the intersecting lines and points that would provide the first evaluation of any instability in an engineering structure characterized by the failure modes. In this work, the i...
متن کاملMore complete intersection theorems
The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families. In recent work, we extended this theorem to the weighted setting, giving the maximum μp measure of a t-intersecting family on n points. In this work, we prove two new complete intersection theorems. The first gi...
متن کاملTowards extending the Ahlswede-Khachatrian theorem to cross t-intersecting families
Ahlswede and Khachatrian's diametric theorem is a weighted version of their complete intersection theorem, which is itself a well known extension of the t-intersecting Erd˝ os-Ko-Rado theorem. The complete intersection theorem says that the maximum size of a family of subsets of [n] = {1,. .. , n}, every pair of which intersects in at least t elements, is the size of certain trivially intersect...
متن کاملThe weighted complete intersection theorem
The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for t ≥ 2. We extend this theorem to the weighted setting, in which we consider unconstrained families. The goal in this setting is to maximize the μp measure of the family, where the measure μp is given by μp(A)...
متن کامل3-Wise Exactly 1-Intersecting Families of Sets
Let f(l,t,n) be the maximal size of a family F ⊂ 2[n] such that any l ≥ 2 sets of F have an exactly t ≥ 1-element intersection. If l ≥ 3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine f(l, t, n) = ⌊ l 2(n− 1) ⌋ +1. Let g(l, t, n) be the maximal size of an l-wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 12 شماره
صفحات -
تاریخ انتشار 2005