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 | |
【 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
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO201912050577059ZK.pdf | 14KB | download |