{"paper":{"title":"Inequalities for the overpartition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edward Y.S. Liu, Helen W.J. Zhang","submitted_at":"2018-08-15T14:16:44Z","abstract_excerpt":"Let $\\overline{p}(n)$ denote the overpartition funtion. Engel showed that for $n\\geq2$, $\\overline{p}(n)$ satisfied the Tur\\'{a}n inequalities, that is, $\\overline{p}(n)^2-\\overline{p}(n-1)\\overline{p}(n+1)>0$ for $n\\geq2$. In this paper, we prove several inequalities for $\\overline{p}(n)$. Moreover, motivated by the work of Chen, Jia and Wang, we find that the higher order Tur\\'{a}n inequalities of $\\overline{p}(n)$ can also be determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05091","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"}