منابع مشابه
Almost-Fisher families
A classic theorem in combinatorial design theory is Fisher’s inequality, which states that a family F of subsets of [n] with all pairwise intersections of size λ can have at most n non-empty sets. One may weaken the condition by requiring that for every set in F , all but at most k of its pairwise intersections have size λ. We call such families k-almost λ-Fisher. Vu was the first to study the ...
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Roughly speaking, an (n, (r, s))-Cover Free Family (CFF) is a small set of n-bit strings such that: “in any d := r+s indices we see all patterns of weight r”. CFFs have been of interest for a long time both in discrete mathematics as part of block design theory, and in theoretical computer science where they have found a variety of applications, for example, in parametrized algorithms where the...
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Let us write DF (G) = {F ∈ F : F ∩ G = ∅} for a set G and a family F . Then a family F of sets is said to be (≤ l)-almost intersecting (l-almost intersecting) if for any F ∈ F we have |DF (F )| ≤ l (|DF (F )| = l). In this paper we investigate the problem of finding the maximum size of an (≤ l)almost intersecting (l-almost intersecting) family F . AMS Subject Classification: 05D05
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2016
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2015.10.003