The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces

In the present paper we investigate the Gromov–Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex’s cardinality does not exceed the cardinality of $X$, a new formula for this distance is obtained. The latter permits to derive an exact formula for the distance between a simplex and an ultrametric space.