{"paper":{"title":"The Pop-Stack Operator on Ornamentation Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin Defant, Khalid Ajran","submitted_at":"2025-01-17T17:27:13Z","abstract_excerpt":"Each rooted plane tree $\\mathsf{T}$ has an associated ornamentation lattice $\\mathcal{O}(\\mathsf{T})$. The ornamentation lattice of an $n$-element chain is the $n$-th Tamari lattice. We study the pop-stack operator $\\mathsf{Pop}\\colon\\mathcal{O}(\\mathsf{T})\\to\\mathcal{O}(\\mathsf{T})$, which sends each element $\\delta$ to the meet of the elements covered by or equal to $\\delta$. We compute the maximum size of a forward orbit of $\\mathsf{Pop}$ on $\\mathcal{O}(\\mathsf{T})$, generalizing a result of Defant for Tamari lattices. We also characterize the image of $\\mathsf{Pop}$ on $\\mathcal{O}(\\maths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.10311","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/2501.10311/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"}