منابع مشابه
Multiply-intersecting families
Intersection problems occupy an important place in the theory of finite sets. One of the central notions is that of a r-wise r-intersecting family, that is, a collection holds for all choices of 1 < il < < i, < m. What is the maximal size m = m(n, r, t) of a r-wise t-intersecting family? Taking all subsets containing a fixed t-element set shows that m(n, r, 1) > 2 "-' holds for all n 3 f 2 0. O...
متن کاملMultiply-intersecting families revisited
Motivated by the Frankl’s results in [11] (“Multiply-intersecting families,” J. Combin. Theory (B) 1991), we consider some problems concerning the maximum size of multiply-intersecting families with additional conditions. Among other results, we show the following version of the Erdős–Ko–Rado theorem: for all r ≥ 8 and 1≤ t ≤ 2r+1−3r−1 there exist positive constants ε and n0 such that if n > n0...
متن کاملMultiply intersecting families of sets
Let [n] denote the set {1, 2, ..., n}, 2 the collection of all subsets of [n] and F ⊂ 2 be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ` subsets containing t+1 common elements. We show that |F| ≤ Pt−s i=0 n−s i + t+`−s t+2−s n−s t+1−s + `− 2 and this bound is asymptotically the best possible as n →∞ and t ≥ 2s ≥ 2, r, ` ≥ 2 a...
متن کاملRandom walks and multiply intersecting families
Let F ⊂ 2 be a 3-wise 2-intersecting Sperner family. It is proved that |F| ≤ { ( n−2 (n−2)/2 ) if n even, ( n−2 (n−1)/2 ) + 2 if n odd holds for n ≥ n0. The unique extremal configuration is determined as well.
متن کاملWeighted 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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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1991
ISSN: 0095-8956
DOI: 10.1016/0095-8956(91)90075-u