{"paper":{"title":"Interlacing Polynomials and the Veronese Construction for Rational Formal Power Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Philip B. Zhang","submitted_at":"2018-06-21T10:51:41Z","abstract_excerpt":"Fixing a positive integer $r$ and $0 \\le k \\le r-1$, define $f^{\\langle r,k \\rangle}$ for every formal power series $f$ as $ f(x) = f^{\\langle r,0 \\rangle}(x^r)+xf^{\\langle r,1 \\rangle}(x^r)+ \\cdots +x^{r-1}f^{\\langle r,r-1 \\rangle}(x^r).$ Jochemko recently showed that the polynomial $U^{n}_{r,k}\\, h(x) := \\left( (1+x+\\cdots+x^{r-1})^{n} h(x) \\right)^{\\langle r,k \\rangle}$ has only nonpositive zeros for any $r \\ge \\deg h(x) -k$ and any positive integer $n$. As a consequence, Jochemko confirmed a conjecture of Beck and Stapledon on the Ehrhart polynomial $h(x)$ of a lattice polytope of dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08165","kind":"arxiv","version":1},"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"}