Patterns in sets of positive density in trees and affine buildings

  • Michael Björklund

    Chalmers University, Gothenburg, Sweden
  • Alexander Fish

    University of Sydney, Australia
  • James Parkinson

    University of Sydney, Australia
Patterns in sets of positive density in trees and affine buildings cover
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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.

Cite this article

Michael Björklund, Alexander Fish, James Parkinson, Patterns in sets of positive density in trees and affine buildings. Groups Geom. Dyn. 15 (2021), no. 4, pp. 1267–1295

DOI 10.4171/GGD/630