{"paper":{"title":"Regularity and Free Resolution of Ideals which are Minimal to $d$-linearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Akbar Yazdan Pour, Marcel Morales, Rashid Zaare-Nahandi","submitted_at":"2012-07-07T12:06:43Z","abstract_excerpt":"Toward a partial classification of monomial ideals with $d$-linear resolution, in this paper, some classes of $d$-uniform clutters which do not have linear resolution, but every proper subclutter of them has a $d$-linear resolution, are introduced and the regularity and Betti numbers of circuit ideals of such clutters are computed. Also, it is proved that for given two $d$-uniform clutters $\\mathcal{C}_1, \\mathcal{C}_2$, the Castelnuovo-Mumford regularity of the ideal $I(\\bar{\\mathcal{C}_1 \\cup \\mathcal{C}_2})$ is equal to the maximum of regularities of $I(\\bar{\\C}_1)$ and $I(\\bar{\\C}_2)$, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1790","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"}