期刊论文详细信息
Canadian mathematical bulletin
Equilateral Sets and a Schütte Theorem for the $4$-norm
Konrad J. Swanepoel1 
[1] Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, United Kingdom
关键词: Ramsey property;    linear orderings;   
DOI  :  10.4153/CMB-2013-031-0
学科分类:数学(综合)
来源: University of Toronto Press * Journals Division
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【 摘 要 】

A well-known theorem of Schütte (1963) gives a sharp lower bound forthe ratio of the maximum and minimum distances between $n+2$ points in$n$-dimensional Euclidean space.In this note we adapt Bárány's elegant proof (1994) of this theorem to the space $ell_4^n$.This gives a new proof that the largest cardinality of an equilateralset in $ell_4^n$ is $n+1$, and gives a constructive bound for aninterval $(4-varepsilon_n,4+varepsilon_n)$ of values of $p$ close to $4$ for which it is known that the largest cardinality of an equilateral set in $ell_p^n$ is $n+1$.

【 授权许可】

Unknown   

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