{"paper":{"title":"A New Characterization of $\\mathcal{V}$-Posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hays Whitlatch, Joshua Cooper, Peter Gartland","submitted_at":"2018-10-16T21:04:24Z","abstract_excerpt":"In 2016, Hasebe and Tsujie gave a recursive characterization of the set of induced $N$-free and bowtie-free posets; Misanantenaina and Wagner studied these orders further, naming them \"$\\mathcal{V}$-posets\". Here we offer a new characterization of $\\mathcal{V}$-posets by introducing a property we refer to as autonomy. A poset $\\cP$ is said to be autonomous if there exists a directed acyclic graph $D$ (with adjacency matrix $U$) whose transitive closure is $\\cP$, with the property that any total ordering of the vertices of $D$ so that Gaussian elimination of $U^TU$ proceeds without row swaps is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07276","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"}