منابع مشابه
Locally Thin Set Families
A family of subsets of an n–set is k–locally thin if for every k of its member sets the ground set has at least one element contained in exactly 1 of them. We derive new asymptotic upper bounds for the maximum cardinality of locally thin set families for every even k. This improves on previous results of two of us with Monti. ∗Research supported in part by a USA Israeli BSF grant and by a grant...
متن کاملA Better Bound for Locally Thin Set Families
A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most 2 members. This improves on our previous results with Noga Alon. The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph ...
متن کاملOn Cancellative Set Families
A family of subsets of an n-set is 2-cancellative if for every four-tuple {A, B, C, D} of its members A ∪B ∪C = A ∪B ∪D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A ∪B 6= A ∪C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known, (Tolhuizen [7]). We provide a new upper ...
متن کاملLocally isometric families of minimal surfaces
We consider a surface M immersed in R with induced metric g = ψδ2 where δ2 is the two dimensional Euclidean metric. We then construct a system of partial differential equations that constrain M to lift to a minimal surface via the Weierstrauss-Enneper representation, demanding the metric is of the above form. It is concluded that the associated surfaces connecting the prescribed minimal surface...
متن کاملFamilies of locally separated Hamilton paths
We improve by an exponential factor the lower bound of Körner and Muzi for the cardinality of the largest family of Hamilton paths in a complete graph of n vertices in which the union of any two paths has degree 4. The improvement is through an explicit construction while the previous bound was obtained by a greedy algorithm. We solve a similar problem for permutations up to an exponential factor.
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2000
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548300004521