{"paper":{"title":"Sharp Poincare-Wirtinger inequalities on complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Cristian Gonz\\'alez-Riquelme, Jos\\'e Madrid","submitted_at":"2024-11-18T21:44:33Z","abstract_excerpt":"Let $K_n=(V,E)$ be the complete graph with $n\\geq 3$ vertices (here $V$ and $E$ denote the set of vertices and edges of $K_n$ respectively). We find the optimal value ${\\bf{C}}_{n,p}$ such that the inequality $$\\|f-m_f\\|_p\\le {\\bf C}_{n,p}{\\rm Var}_{p}f$$ holds for every $f:V\\to \\mathbb{R},$ where ${\\rm Var}_p$ stands for the $p$-variation, and $m_f$ stands for the average value of $f$, for all $p\\in[1,3+\\delta^1_n)\\cup (3+\\delta^2_n,+\\infty)$, for $\\delta^1_n=\\frac{1}{2n^2\\log(n)}+O(1/n^3)$ and $\\delta^2_n=\\frac{2}{n}+O(1/n^2).$ Moreover, we characterize all the maximizer functions in that ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12079","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/2411.12079/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"}