{"paper":{"title":"On semigroup rings with decreasing Hilbert function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anna Oneto, Grazia Tamone","submitted_at":"2016-01-31T21:36:57Z","abstract_excerpt":"In this paper we study the Hilbert function HR of one-dimensional semigroup rings R = k[[S]]. For some classes of semigroups, by means of the notion of support of the elements in S, we give conditions on the generators of S in order to have decreasing HR. When the embedding dimension v and the multiplicity e verify v + 3 ? e ? v + 4, the decrease of HR gives explicit description of the Apery set of S. In particular for e = v+3, we classify the semigroups with e = 13 and HR decreasing, further we show that HR is non-decreasing if e < 12. Finally we deduce that HR is non-decreasing for every Gor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00327","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"}