{"paper":{"title":"$h^*$-Polynomials With Roots on the Unit Circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Benjamin Braun, Fu Liu","submitted_at":"2018-06-30T01:55:22Z","abstract_excerpt":"For an $n$-dimensional lattice simplex $\\Delta_{(1,\\mathbf{q})}$ with vertices given by the standard basis vectors and $-\\mathbf{q}$ where $\\mathbf{q}$ has positive entries, we investigate when the Ehrhart $h^*$-polynomial for $\\Delta_{(1,\\mathbf{q})}$ factors as a product of geometric series in powers of $z$. Our motivation is a theorem of Rodriguez-Villegas implying that when the $h^*$-polynomial of a lattice polytope $P$ has all roots on the unit circle, then the Ehrhart polynomial of $P$ has positive coefficients. We focus on those $\\Delta_{(1,\\mathbf{q})}$ for which $\\mathbf{q}$ has only "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00105","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"}