We pursue the investigation of the concept of $n$-distance, an $n$-variable version of the classical concept of distance recently introduced and investigated by Kiss, Marichal, and Teheux. We especially focus on the challenging problem of computing the best constant associated with a given $n$-distance. In particular, we define and investigate the best constants related to partial simplex inequalities. We also introduce and discuss some subclasses of $n$-distances defined by considering some properties. Finally, we discuss an interesting link between the concepts of $n$-distance and multidistance.

中文翻译：

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关于与 n 距离相关的最佳常数

我们继续研究 $n$-distance 的概念，这是最近由 Kiss、Marichal 和 Teheux 引入和研究的经典距离概念的 $n$-variable 版本。我们特别关注计算与给定 $n$-距离相关的最佳常数的挑战性问题。特别是，我们定义并研究了与偏单纯形不等式相关的最佳常数。我们还介绍和讨论了通过考虑一些属性定义的 $n$-distances 的一些子类。最后，我们讨论 $n$-distance 和 multidistance 概念之间的有趣联系。