A note on high-dimensional discrepancy of subtrees Hollom, Lawrence Lichev, Lyuben Mond, Adva Portier, Julien Trees High-dimensional discrepancy Oriented discrepancy For a tree T and a function f:E(T)→Sd, the imbalance of a subtree T′⊆T is given by |∑e∈E(T′)f(e)|. The d-dimensional discrepancy of the tree T is the minimum, over all functions f as above, of the maximum imbalance of a subtree of T. We prove tight asymptotic bounds for the discrepancy of a tree T, confirming a conjecture of Krishna, Michaeli, Sarantis, Wang and Wang. We also settle a related conjecture on oriented discrepancy of subtrees by the same authors. Springer 2026 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/23158 Hollom L, Lichev L, Mond A, Portier J. A note on high-dimensional discrepancy of subtrees. <i>Discrete and Computational Geometry</i>. 2026. doi:<a href="https://doi.org/10.1007/s00454-025-00790-x">10.1007/s00454-025-00790-x</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00454-025-00790-x info:eu-repo/semantics/altIdentifier/issn/0179-5376 info:eu-repo/semantics/altIdentifier/e-issn/1432-0444 info:eu-repo/semantics/altIdentifier/arxiv/2412.04170 info:eu-repo/semantics/openAccess