Geodesic
Patterns in sets of positive density in trees and affine buildings
Michael Björklund1 ; Alexander Fish2 ; James Parkinson2
1Chalmers University, Gothenburg, Sweden
2University of Sydney, Australia
Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1267-1295

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DOI

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.
DOI : 10.4171/ggd/630
Classification : 05-XX
Mots-clés : Density, Ramsey theory on trees and buildings

Michael Björklund  1   ; Alexander Fish  2   ; James Parkinson  2

1 Chalmers University, Gothenburg, Sweden
2 University of Sydney, Australia 
Michael Björklund; Alexander Fish; James Parkinson. Patterns in sets of positive density in trees and affine buildings. Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1267-1295. doi: 10.4171/ggd/630
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     title = {Patterns in sets of positive density in trees and affine buildings},
     journal = {Groups, geometry, and dynamics},
     pages = {1267--1295},
     year = {2021},
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     number = {4},
     doi = {10.4171/ggd/630},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/630/}
}
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