{"paper":{"title":"The converse of a theorem by Bayer and Stillman","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"HyunBin Loh","submitted_at":"2014-10-22T09:49:10Z","abstract_excerpt":"Bayer-Stillman showed that $reg(I) = reg(gin_\\tau(I))$ when $\\tau$ is the graded reverse lexicographic order. We show that the reverse lexicographic order is the unique monomial order $\\tau$ satisfying $reg(I) = reg(gin_\\tau(I))$ for all ideals $I$. We also show that if $gin_{\\tau_1}(I) = gin_{\\tau_2}(I)$ for all $I$, then $\\tau_1 = \\tau_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5969","kind":"arxiv","version":2},"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"}