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The Universal 𝓁^p-Metric on Merge Trees Cardona, Robert Curry, Justin Lam, Tung Lesnick, Michael merge trees hierarchical clustering persistent homology Wasserstein distances interleavings Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an 𝓁^p-type extension of the interleaving distance on merge trees. We show that our distance is a metric, and that it upper-bounds the p-Wasserstein distance between the associated barcodes. For each p ∈ [1,∞], we prove that this distance is stable with respect to cellular sublevel filtrations and that it is the universal (i.e., largest) distance satisfying this stability property. In the p = ∞ case, this gives a novel proof of universality for the interleaving distance on merge trees. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Robert Cardona and Justin Curry and Tung Lam and Michael Lesnick 2022 Is Part Of LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2022.24 urn:nbn:de:0030-drops-160325 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.24 eng https://creativecommons.org/licenses/by/4.0/legalcode