Structure and Supersaturation for Intersecting Families
نویسندگان
چکیده
منابع مشابه
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...
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When t = 1, we simply say that the family is intersecting. Consider the following example. Fix a t-set, say I ⊆ [n], and values {xi : i ∈ I}. If for every σ ∈ F and i ∈ I σ(i) = xi, then F is clearly t-intersecting. Furthermore, we say that F is a trivial t-intersecting family of permutations. Note that the size of this family is at most (n − t)!. Ellis, Friedgut, and Pilpel [5] show that for n...
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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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A family A of sets is said to be intersecting if A ∩ B 6= ∅ for all A, B ∈ A. It is a well-known and simple fact that an intersecting family of subsets of [n] = {1, 2, . . . , n} can contain at most 2n−1 sets. Katona, Katona and Katona ask the following question. Suppose instead A ⊂ P[n] satisfies |A| = 2n−1 + i for some fixed i > 0. Create a new family Ap by choosing each member of A independe...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7683