{"paper":{"title":"Finite palette endpoints and degree-square Tur\\'an problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Chen, Jiangdong Ai, Ming Chen, Tianxiao Zhao, Zilong Yan","submitted_at":"2026-06-02T11:42:17Z","abstract_excerpt":"We study finite extremal problems for palettes, which arise from the palette framework for the uniform Tur\\'an densities of $3$-uniform hypergraphs. Recent work has developed reductions from palette colorability questions to extremal problems for digraphs. In this paper we prove an exact degree-square refinement of these reductions for a natural family of left and right tournament palettes.\n  For a tournament $T$, let $P_T^L$ and $P_T^R$ denote the left and right palettes generated by $T$. We prove that if $T$ is self-converse and has at least two vertices, then for every $m\\ge 1$ the maximum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03520","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/2606.03520/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"}