{"paper":{"title":"Antichain Simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Brian Davis","submitted_at":"2019-01-05T14:02:13Z","abstract_excerpt":"To each lattice simplex $\\Delta$ we associate a poset encoding the additive structure of lattice points in the fundamental parallelepiped for $\\Delta$. When this poset is an antichain, we say $\\Delta$ is antichain. To each partition $\\lambda$ of $n$, we associate a lattice simplex $\\Delta_\\lambda$ having one unimodular facet, and we investigate their associated posets. We give a number-theoretic characterization of the relations in these posets, as well as a simplified characterization in the case where each part of $\\lambda$ is relatively prime to $n-1$. We use these characterizations to expe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01417","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"}