{"paper":{"title":"Chordality of Clutters with Vertex Decomposable Dual and Ascent of Clutters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ashkan Nikseresht","submitted_at":"2017-08-24T12:28:29Z","abstract_excerpt":"In this paper, we consider the generalization of chordal graphs to clutters proposed by Bigdeli, et al in J. Combin. Theory, Series A (2017). Assume that $\\mathcal{C}$ is a $d$-dimensional uniform clutter. It is known that if $\\mathcal{C}$ is chordal, then $I(\\bar{\\mathcal{C}})$ has a linear resolution over all fields. The converse has recently been rejected, but the following question which poses a weaker version of the converse is still open: \"if $I(\\bar{\\mathcal{C}})$ has linear quotients, is $\\mathcal{C}$ necessarily chordal?\". Here, by introducing the concept of the ascent of a clutter, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07372","kind":"arxiv","version":3},"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"}