{"paper":{"title":"On the Poset of Multichains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle","submitted_at":"2015-06-13T14:59:31Z","abstract_excerpt":"In this note we introduce the poset of $m$-multichains of a given poset $\\mathcal{P}$. Its elements are the multichains of $\\mathcal{P}$ consisting of $m$ elements, and its partial order is the componentwise partial order of $\\mathcal{P}$. We show that this construction preserves a number of poset-theoretic and poset-topological properties of $\\mathcal{P}$. Moreover, we describe the structure of the poset of $m$-multichains of a finite distributive lattice, and provide a link to R.~Stanley's theory of $\\mathcal{P}$-partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04276","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"}