{"paper":{"title":"Gapfree graphs and powers of edge ideals with linear quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Nursel Erey, Sara Faridi, Selvi Kara, Susan Morey, T\\`ai Huy H\\`a, Takayuki Hibi","submitted_at":"2024-12-09T13:12:10Z","abstract_excerpt":"Let $I(G)$ be the edge ideal of a gapfree graph $G$. An open conjecture of Nevo and Peeva states that $I(G)^q$ has linear resolution for $q\\gg 0$. We present a promising approach to this challenging conjecture by investigating the stronger property of linear quotients. Specifically, we make the conjecture that if $I(G)^q$ has linear quotients for some integer $q\\geq 1$, then $I(G)^{s}$ has linear quotients for all $s\\geq q$. We give a partial solution to this conjecture, and identify conditions under which only finitely many powers need to be checked. It is known that if $G$ does not contain a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06467","kind":"arxiv","version":2},"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/2412.06467/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"}