Geodesic
Equilateral Sets and a Schütte Theorem forthe 4-norm
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 640-647

Voir la notice de l'article provenant de la source Cambridge University Press

A well-known theorem of Schütte (1963) gives a sharp lower bound for the 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 equilateral set in $\ell _{4}^{n}$ is $n\,+\,1$ and gives a constructive bound for an interval $\left( 4\,-\,{{\varepsilon }_{n}},\,4\,+\,{{\varepsilon }_{n}} \right)$ 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 $n\,+\,1$ .
DOI : 10.4153/CMB-2013-031-0
Mots-clés : 46B20, 52A21, 52C17 
Swanepoel, Konrad J. Equilateral Sets and a Schütte Theorem forthe 4-norm. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 640-647. doi: 10.4153/CMB-2013-031-0
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