[{"publisher":"Springer","abstract":[{"text":"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.","lang":"eng"}],"author":[{"last_name":"Hollom","first_name":"Lawrence","full_name":"Hollom, Lawrence"},{"last_name":"Lichev","first_name":"Lyuben","id":"9aa8388e-d003-11ee-8458-c4c1d7447977","full_name":"Lichev, Lyuben"},{"full_name":"Mond, Adva","first_name":"Adva","last_name":"Mond"},{"full_name":"Portier, Julien","first_name":"Julien","last_name":"Portier"}],"oa":1,"quality_controlled":"1","OA_type":"green","status":"public","scopus_import":"1","researchdata_availability":"no","publication":"Discrete and Computational Geometry","year":"2026","date_updated":"2026-10-19T08:20:42Z","das_tickbox":"1","acknowledgement":"The authors would like to thank both Béla Bollobás and the anonymous reviewer for their careful readings of the manuscript and for their valuable comments. The first author was funded by Trinity College, Cambridge. The second author was funded in whole or in part by the Austrian Science Fund (FWF) 10.55776/ESP624. The third author was supported by UK Research and Innovation grant MR/W007320/2. The fourth author was funded by EPSRC (Engineering and Physical Sciences Research Council) and by the Cambridge Commonwealth, European and International Trust.","date_created":"2026-10-18T22:01:53Z","department":[{"_id":"MaKw"}],"date_published":"2026-10-09T00:00:00Z","dataavailabilitystatement":"Data sharing not applicable to this article as no datasets were generated or analysed during the current study.","OA_place":"repository","supplementarymaterial":"no","month":"10","arxiv":1,"article_type":"original","mathsc":["05C05","05C35","11K38"],"project":[{"grant_number":"E624","name":"THRESHOLDS IN SEMI-RANDOM PROCESSES AND GRAPH EMBEDDINGS","_id":"e19fef4c-1f3d-11f0-ac04-b8b1af6886d8"}],"type":"journal_article","article_processing_charge":"No","doi":"10.1007/s00454-025-00790-x","oa_version":"Preprint","fulldoi":"https://doi.org/10.1007/s00454-025-00790-x","language":[{"iso":"eng"}],"_id":"23158","keyword":["Trees","High-dimensional discrepancy","Oriented discrepancy"],"day":"09","citation":{"chicago":"Hollom, Lawrence, Lyuben Lichev, Adva Mond, and Julien Portier. “A Note on High-Dimensional Discrepancy of Subtrees.” <i>Discrete and Computational Geometry</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s00454-025-00790-x\">https://doi.org/10.1007/s00454-025-00790-x</a>.","ista":"Hollom L, Lichev L, Mond A, Portier J. 2026. A note on high-dimensional discrepancy of subtrees. Discrete and Computational Geometry.","ama":"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>","short":"L. Hollom, L. Lichev, A. Mond, J. Portier, Discrete and Computational Geometry (2026).","ieee":"L. Hollom, L. Lichev, A. Mond, and J. Portier, “A note on high-dimensional discrepancy of subtrees,” <i>Discrete and Computational Geometry</i>. Springer, 2026.","mla":"Hollom, Lawrence, et al. “A Note on High-Dimensional Discrepancy of Subtrees.” <i>Discrete and Computational Geometry</i>, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s00454-025-00790-x\">10.1007/s00454-025-00790-x</a>.","apa":"Hollom, L., Lichev, L., Mond, A., &#38; Portier, J. (2026). A note on high-dimensional discrepancy of subtrees. <i>Discrete and Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-025-00790-x\">https://doi.org/10.1007/s00454-025-00790-x</a>"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2412.04170","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","publication_identifier":{"eissn":["1432-0444"],"issn":["0179-5376"]},"external_id":{"arxiv":["2412.04170"]},"title":"A note on high-dimensional discrepancy of subtrees"}]