{"paper":{"title":"On the Log-Concavity of Hilbert Series of Veronese Subrings and Ehrhart Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan Stapledon, Matthias Beck","submitted_at":"2008-04-23T04:20:32Z","abstract_excerpt":"For every positive integer $n$, consider the linear operator $\\U_{n}$ on polynomials of degree at most $d$ with integer coefficients defined as follows: if we write $\\frac{h(t)}{(1 - t)^{d + 1}} = \\sum_{m \\geq 0} g(m) t^{m}$, for some polynomial $g(m)$ with rational coefficients, then $\\frac{\\U_{n}h(t)}{(1- t)^{d + 1}} = \\sum_{m \\geq 0} g(nm) t^{m}$. We show that there exists a positive integer $n_{d}$, depending only on $d$, such that if $h(t)$ is a polynomial of degree at most $d$ with nonnegative integer coefficients and $h(0) \\geq 1$, then for $n \\geq n_{d}$, $\\U_{n}h(t)$ has simple, real,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3639","kind":"arxiv","version":3},"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"}