{"paper":{"title":"The $m$-Cover Posets and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle, Myrto Kallipoliti","submitted_at":"2013-12-09T17:26:06Z","abstract_excerpt":"In this article we introduce the $m$-cover poset of an arbitrary bounded poset $\\mathcal{P}$, which is a certain subposet of the $m$-fold direct product of $\\mathcal{P}$ with itself. Its ground set consists of multichains of $\\mathcal{P}$ that contain at most three different elements, one of which has to be the least element of $\\mathcal{P}$, and the other two elements have to form a cover relation in $\\mathcal{P}$. We study the $m$-cover poset from a structural and topological point of view. In particular, we characterize the posets whose $m$-cover poset is a lattice for all $m>0$, and we cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2520","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"}