{"paper":{"title":"$h$-vectors of edge rings of odd-cycle compositions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Akihiro Higashitani, Kieran Bhaskara, Nayana Shibu Deepthi","submitted_at":"2023-11-22T18:27:48Z","abstract_excerpt":"Let $\\mathbb{K}[G]$ be the edge ring of a finite simple graph $G$. Investigating properties of the $h$-vector of $\\mathbb{K}[G]$ is of great interest in combinatorial commutative algebra. However, there are few families of graphs for which the $h$-vector has been explicitly determined. In this paper, we compute the $h$-vectors of a certain family of graphs that satisfy the odd-cycle condition, generalizing a result of the second and third named authors. As a corollary, we obtain a characterization of the graphs in this family whose edge rings are almost Gorenstein."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13573","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/2311.13573/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"}