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arXiv · 1907.05825

Patterns in sets of positive density in trees and affine buildings

M. Björklund·A. Fish·J. Parkinson
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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.

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M. Björklund, A. Fish, J. Parkinson. 2019-07-12. Patterns in sets of positive density in trees and affine buildings. https://arxiv.org/abs/1907.05825

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