Maximal Equilateral Sets
نویسندگان
چکیده
منابع مشابه
Maximal Equilateral Sets
A subset of a normed space X is called equilateral if the distance between any two points is the same. Let m(X) be the smallest possible size of an equilateral subset of X maximal with respect to inclusion. We first observe that Petty’s construction of a d-dimensional X of any finite dimension d ≥ 4 with m(X) = 4 can be generalised to show that m(X⊕1 R) = 4 for any X of dimension at least 2 whi...
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If X is a Minkowski space, i.e. a finite dimensional real normed space, then S ⊂ X is an equilateral set if all pairs of points of S determine the same distance with respect to the norm. Kusner conjectured that e(`p) = d +1 for 1 < p < ∞ and e(`1) = 2d [6]. Using a technique combining linear algebra and approximation theory, we prove that for all 1 < p < ∞, there exists a constant Cp > 0 such t...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2013
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-013-9523-z