{"paper":{"title":"The Briggs inequality for partitions and overpartitions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xin-Bei Liu, Zhong-Xue Zhang","submitted_at":"2024-08-29T00:49:36Z","abstract_excerpt":"A sequence of $\\{a_n\\}_{n\\ge 0}$ satisfies the Briggs inequality if \\begin{align*} a_n^2(a_n^2-a_{n-1}a_{n+1})>a_{n-1}^2(a_{n+1}^2-a_na_{n+2}) \\end{align*} holds for any $n\\ge 1$. In this paper we show that both the partition function $\\{p(n+N_0)\\}_{n\\geq 0}$ and the overpartition function $\\{\\overline{p}(n+\\overline{N}_0)\\}_{n\\ge 0}$ satisfy the Briggs inequality for some $N_0$ and $\\overline{N}_{0}$. Based on Chern's formula for $\\eta$-quotients, we further prove that the $k$-regular partition function $\\{p_k(n+N_{k})\\}_{n\\geq 0}$ and the $k$-regular overpartition function $\\{\\overline{p}_k("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.16185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}