This is an announcement for the paper "Distortion of embeddings of binary trees into diamond graphs" by Siu Lam Leung, Sarah Nelson, Sofiya Ostrovska, and Mikhail Ostrovskii.
Abstract: Diamond graphs and binary trees are important examples in the theory of metric embeddings and also in the theory of metric characterizations of Banach spaces. Some results for these families of graphs are parallel to each other, for example superreflexivity of Banach spaces can be characterized both in terms of binary trees (Bourgain, 1986) and diamond graphs (Johnson-Schechtman, 2009). In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. This question was answered in the negative by Ostrovskii (2014), who left it open to determine the order of growth of the distortions. The main purpose of this paper is to get a sharp-up-to-a-logarithmic-factor estimate for the distortions of embeddings of binary trees into diamond graphs.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 05C12, 30L05, 46B85
Submitted from: ostrovsm@stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.06438
or