{"paper":{"title":"Order Preserving Maps of Posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Suijie Wang, Zhousheng Mei","submitted_at":"2017-09-05T04:27:24Z","abstract_excerpt":"For any two finite posets $P$ and $Q$, let $\\Hom(P,Q)$ be the hom-poset consisting of all order preserving maps from $P$ to $Q$, and $J(Q)$ the collection of all order ideals of $Q$. In this paper, we study some basic properties of the hom-poset $\\Hom(P,Q)$ and prove that $\\Hom\\big(P,J(Q)\\big)$ is a distributive lattice and characterized by \\[ \\Hom\\big(P,J(Q)\\big)\\cong J(P^*\\times Q), \\] where $P^*$ is the dual of $P$. Consequently, we obtain that $\\Hom\\big(P,J(Q)\\big)$ and $\\Hom\\big(Q,J(P)\\big)$ are dual isomorphic, i.e., \\[ \\Hom\\big(P,J(Q)\\big)\\cong \\Hom^{*}\\big(Q,J(P)\\big). \\] As applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01234","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"}