{"paper":{"title":"Artinian level algebras of socle degree 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maria Evelina Rossi, Shreedevi K. Masuti","submitted_at":"2017-01-11T22:26:59Z","abstract_excerpt":"In this paper we study the O-sequences of the local (or graded) $K$-algebras of socle degree $4.$ More precisely, we prove that an O-sequence $h=(1, 3, h_2, h_3, h_4)$, where $h_4 \\geq 2,$ is the $h$-vector of a local level $K$-algebra if and only if $h_3\\leq 3 h_4.$ We also prove that $h=(1, 3, h_2, h_3, 1)$ is the $h$-vector of a local Gorenstein $K$-algebra if and only if $h_3 \\leq 3$ and $h_2 \\leq \\binom{h_3+1}{2}+(3-h_3).$ In each of these cases we give an effective method to construct a local level $K$-algebra with a given $h$-vector. Moreover we refine a result by Elias and Rossi by sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03180","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"}