{"paper":{"title":"Stolarsky-Type Inequalities in a Max-Convolution Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johannes Hosle","submitted_at":"2026-06-06T02:33:58Z","abstract_excerpt":"For $m \\in \\mathbb{N}$, let $q_m := \\frac{\\log(2m+1)}{2\\log(m+1)}$. The max-convolution inequality \\begin{align*}\n  \\sum_{k=0}^{2m}\\left(\\max_{i+j=k} x_i y_j \\right)^{q_m} &\\ge \\left(\\sum_{i=0}^{m} x_i\\right)^{q_m} \\left(\\sum_{j=0}^{m} y_j\\right)^{q_m} \\end{align*}for arbitrary sequences $x_0 \\ge x_1 \\ge ... \\ge x_m \\ge 0, y_0 \\ge y_1 \\ge ... \\ge y_m \\ge 0$ implies an affirmative answer to a question of Bourgain, Dilworth, Ford, Konyagin, and Kutzarova \\cite{BDFKK} on the sizes of sumsets in product sets. This inequality was proven for $m = 2$ by Becker, Ivanisvili, Krachun, and Madrid \\cite{B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07946","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/2606.07946/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"}