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] : |...
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The study of intersecting structures is central to extremal combinatorics. A family of permutations F ⊂ Sn is t-intersecting if any two permutations in F agree on some t indices, and is trivial if all permutations in F agree on the same t indices. A k-uniform hypergraph is tintersecting if any two of its edges have t vertices in common, and trivial if all its edges share the same t vertices. Th...
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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 − ...
متن کاملRegular Intersecting Families
We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families F of k-element subsets of [n] := {1, . . . , n}, such that every element of [n] lies in the same (or approximately the same) number of members of F . In particular, we show that we can guarantee |F| = o( ( n−1 k−1 ) ) if and only if k = o(n).
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90121-4