{"paper":{"title":"Recursive Betti numbers for Cohen-Macaulay $d$-partite clutters arising from posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Davide Bolognini","submitted_at":"2014-11-20T18:15:43Z","abstract_excerpt":"A natural extension of bipartite graphs are $d$-partite clutters, where $d \\geq 2$ is an integer. For a poset $P$, Ene, Herzog and Mohammadi introduced the $d$-partite clutter $\\mathcal{C}_{P,d}$ of multichains of length $d$ in $P$, showing that it is Cohen-Macaulay. We prove that the cover ideal of $\\mathcal{C}_{P,d}$ admits an $x_i$-splitting, determining a recursive formula for its Betti numbers and generalizing a result of Francisco, H\\`a and Van Tuyl on the cover ideal of Cohen-Macaulay bipartite graphs. Moreover we prove a Betti splitting result for the Alexander dual of a Cohen-Macaulay"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5629","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"}