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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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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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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The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more libera...
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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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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1916
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1916-02798-4