{"paper":{"title":"Candidates for non-zero Betti numbers of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AC","authors_text":"Ali Akbar Yazdan Pour","submitted_at":"2015-07-26T11:23:50Z","abstract_excerpt":"Let $I$ be a monomial ideal in the polynomial ring $S$ generated by elements of degree at most $d$. In this paper, it is shown that, if the $i$-th syzygy of $I$ has no element of degrees $j, \\ldots, j+(d-1)$ (where $j \\geq i+d$), then $(i+1)$-syzygy of $I$ does not have any element of degree $j+d$. Then we give several applications of this result, including an alternative proof for Green-Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fr\\\"oberg's theorem on classification of square-free monomial ideals generated in degree two with linear resolution. Among all,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07188","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"}