Abstract
Furstenberg-Weiss have extended Szemerédi’s theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We study higher dimensional versions that analogously extend the multidimensional Szemerédi theorem by demonstrating the existence of certain arithmetic structures in large subsets of a cartesian product of trees.
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Acknowledgement
The authors were partially supported by the Australian Research Council grant DP210100162. The authors are grateful to the anonymous referee for providing useful comments.
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Bulinski, K., Fish, A. Arithmetic subtrees in large subsets of products of trees. JAMA 150, 359–381 (2023). https://doi.org/10.1007/s11854-023-0277-0
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DOI: https://doi.org/10.1007/s11854-023-0277-0