The structure of large non-trivial t-intersecting families of finite sets

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weighted Non-Trivial Multiply Intersecting Families

Let n,r and t be positive integers. A family F of subsets of [n]={1,2, . . . ,n} is called r-wise t-intersecting if |F1∩·· ·∩Fr|≥ t holds for all F1, . . . ,Fr ∈F . An r-wise 1-intersecting family is also called an r-wise intersecting family for short. An r-wise t-intersecting family F is called non-trivial if |⋂F∈F F |<t. Let us define the Brace–Daykin structure as follows. F BD = {F ⊂ [n] : |...

متن کامل

Non-trivial intersecting uniform sub-families of hereditary families

For a family F of sets, let μ(F) denote the size of a smallest set in F that is not a subset of any other set in F , and for any positive integer r, let F (r) denote the family of r-element sets in F . We say that a family A is of Hilton-Milner (HM ) type if for some A ∈ A, all sets in A\{A} have a common element x / ∈ A and intersect A. We show that if a hereditary family H is compressed and μ...

متن کامل

On cross t-intersecting families of sets

For all p, t with 0 < p < 0.11 and 1≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n > n0 and k/n = p the following holds: if A and B are k-uniform families on n vertices, and |A∩B| ≥ t holds for all A ∈A and B ∈B, then |A ||B| ≤ (n−t k−t )2 .

متن کامل

The Intersection Structure of t-Intersecting Families

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.

متن کامل

Structure and properties of large intersecting families

We say that a family of k-subsets of an n-element set is intersecting, if any two of its sets intersect. In this paper we study different extremal properties of intersecting families, as well as the structure of large intersecting families. We also give some results on k-uniform families without s pairwise disjoint sets, related to Erdős Matching Conjecture. We prove a conclusive version of Fra...

متن کامل

ذخیره 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: 2021

ISSN: 0195-6698

DOI: 10.1016/j.ejc.2021.103373