{"paper":{"title":"Rowmotion on hook and two-row alt $\\nu$-Tamari lattices","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sen-Peng Eu, Vei-Cheng Hioe, Yi-Lin Lee","submitted_at":"2026-05-28T06:27:09Z","abstract_excerpt":"In 2024, Ceballos and Chenevi{\\`e}re introduced alt $\\nu$-Tamari lattices, parameterized by a lattice path $\\nu$ and an increment vector $\\delta$, as a common generalization of $\\nu$-Tamari and $\\nu$-Dyck lattices. We study rowmotion on two families: the alt hook-Tamari lattice $\\mathsf{H}_{\\delta}(a,b)$ (where $\\nu=EN^{a-1}E^{b-1}N$) and the alt $2$-row-Tamari lattice $\\mathsf{T}_{\\delta}(a,b)$ (where $\\nu=E^aNE^bN$).\n  We explicitly determine the orbit structures of $\\mathsf{H}_{\\delta}(a,b)$ and $\\mathsf{T}_{\\delta}(a,b)$ under rowmotion, and prove that their orbit structures are independen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29431","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29431/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}