English

Geometric Ruzsa triangle inequality in metric spaces with dilations

Combinatorics 2016-09-22 v2 Metric Geometry

Abstract

The Appendix of the article arXiv:1212.5056 [math.CO] "On growth in an abstract plane" by Nick Gill, H. A. Helfgott, Misha Rudnev, contains a general "geometric Ruzsa triangle inequality" in a Desarguesian projective plane. The purpose of this note is to give a similar inequality for metric spaces with dilations, that is in the absence of an algebraic or incidence structure.

Keywords

Cite

@article{arxiv.1304.3358,
  title  = {Geometric Ruzsa triangle inequality in metric spaces with dilations},
  author = {Marius Buliga},
  journal= {arXiv preprint arXiv:1304.3358},
  year   = {2016}
}

Comments

extended version, detailed proofs, graph rewrites on binary trees used for a short proof of lemma 2