Consider a function $f$ from reals to reals such that $f$, when applied to pairwise Manhattan distances between $n$ points, always results in a set of Manhattan distances.
Work by Schoenberg and Assouad show that any Bernstein function has this property (see Theorem 9.0.3 in the book “Geometry of cuts and metrics”, by Deza and Laurent). Recently, some collaborators and I showed that only Bernstein functions have this property. We published this on arXiv just now.
My question is: was this known before?
