{"paper":{"title":"Sortable simplicial complexes and their associated toric rings","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Somayeh Moradi","submitted_at":"2024-12-13T12:53:51Z","abstract_excerpt":"Let $\\Gamma$ be a $d$-flag sortable simplicial complex. We consider the toric ring $R_{\\Gamma}=K[{\\bf x}_Ft:F\\in \\Gamma]$ and the Rees algebra of the facet ideals $I(\\Gamma^{[i]})$ of pure skeletons of $\\Gamma$. We show that these algebras are Koszul, normal Cohen-Macaulay domains. Moreover, we study the Gorenstein property, the canonical module, and the $a$-invariant of the normal domain $R_{\\Gamma}$ by investigating its divisor class group. Finally, it is shown that any $d$-flag sortable simplicial complex is vertex decomposable, which provides a characterization of the Cohen-Macaulay proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10113","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/2412.10113/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"}