{"paper":{"title":"Alon-Tarsi for hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Bart{\\l}omiej Bosek, Grzegorz Gutowski, Jakub Przyby{\\l}o, Llu\\'is Vena, Marcin Anholcer, Mariusz Zaj\\k{a}c, Micha{\\l} Laso\\'n, Micha{\\l} Tuczy\\'nski, Oriol Serra","submitted_at":"2024-12-30T22:02:05Z","abstract_excerpt":"Given a hypergraph $H=(V,E)$, define for every edge $e\\in E$ a linear expression with arguments corresponding with the vertices. Next, let the polynomial $p_H$ be the product of such linear expressions for all edges. Our main goal was to find a relationship between the Alon-Tarsi number of $p_H$ and the edge density of $H$. We prove that $AT(p_H)=\\lceil ed(H)\\rceil+1$ if all the coefficients in $p_H$ are equal to $1$. Our main result is that, no matter what those coefficients are, they can be permuted within the edges so that for the resulting polynomial $p_H^\\prime$, $AT(p_H^\\prime)\\leq 2\\lce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00157","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/2501.00157/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"}