{"paper":{"title":"Hilbert regularity of ZZ-graded modules over polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jan Uliczka, Julio Jos\\'e Moyano-Fern\\'andez, Winfried Bruns","submitted_at":"2013-08-13T17:08:19Z","abstract_excerpt":"Let M be a finitely generated ZZ-graded module over the standard graded polynomial ring R=K[X_1, ..., X_n] with K a field, and let H_M(t)=Q_M(t)/(1-t)^d be the Hilbert series of M. We introduce the Hilbert regularity of M as the lowest possible value of the Castelnuovo-Mumford regularity for an R-module with Hilbert series H_M. Our main result is an arithmetical description of this invariant which connects the Hilbert regularity of M to the smallest k such that the power series Q_M(1-t)/(1-t)^k has no negative coefficients. Finally we give an algorithm for the computation of the Hilbert regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2917","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":""},"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"}