منابع مشابه
Separated finitely supported $Cb$-sets
The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...
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A set A ⊆ {1, 2, . . . , n} is said to be k-separated if, when considered on the circle, any two elements of A are separated by a gap of size at least k. We prove a conjecture due to Holroyd and Johnson [3],[4] that an analogue of the Erdős-Ko-Rado theorem holds for k-separated sets. In particular the result holds for the vertex-critical subgraph of the Kneser graph identified by Schrijver [7],...
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Let S be a set of n points in R2. Given an integer 1 ≤ k ≤ n, we wish to find a maximally separated subset I ⊆ S of size k; this is a subset for which the minimum among the (k 2 ) pairwise distances between its points is as large as possible. The decision problem associated with this problem is to determine whether there exists I ⊆ S, |I| = k, so that all (k 2 ) pairwise distances in I are at l...
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Erdős posed the following problem. Consider an equicolored point set of 2n points, n points red and n points blue, in the plane in convex position. We estimate the minimal number of points on the longest noncrossing path such that edges join points of different color and are straight line segments. The upper bound 4 3 n + O( √ n) is proved [7], [5] and is conjectured to be tight. The best known...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1973
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-83-1-25-33