{"paper":{"title":"The homological shift algebra of a monomial ideal","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Ayesha Asloob Qureshi","submitted_at":"2024-12-30T15:57:47Z","abstract_excerpt":"Let $S=K[x_1,\\dots,x_n]$ be the polynomial ring over a field $K$, and let $I\\subset S$ be a monomial ideal. In this paper, we introduce the $i$th \\textit{homological shift algebras} $\\text{HS}_i(\\mathcal{R}(I))=\\bigoplus_{k\\ge1}\\text{HS}_i(I^k)$ of $I$. If $I$ has linear powers, these algebras have the structure of a finitely generated bigraded module over the Rees algebra $\\mathcal{R}(I)$ of $I$. Hence, many invariants of $\\text{HS}_i(I^k)$, such as depth, associated primes, regularity, and the $\\text{v}$-number, exhibit well behaved asymptotic behavior. We determine several families of monom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21031","kind":"arxiv","version":3},"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/2412.21031/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"}