Patterns in sets of positive density in trees and affine buildings
Combinatorics
2019-07-15 v1
Abstract
We prove an analogue for homogeneous trees and certain affine buildings of a result of Bourgain on pinned distances in sets of positive density in Euclidean spaces. Furthermore, we construct an example of a non-homogeneous tree with positive Hausdorff dimension, and a subset with positive density thereof, in which not all sufficiently large (even) distances are realised.
Keywords
Cite
@article{arxiv.1907.05825,
title = {Patterns in sets of positive density in trees and affine buildings},
author = {M. Björklund and A. Fish and J. Parkinson},
journal= {arXiv preprint arXiv:1907.05825},
year = {2019}
}