{"paper":{"title":"Nearly subadditive sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Z. Ruzsa, Zoltan Furedi","submitted_at":"2018-10-27T22:20:49Z","abstract_excerpt":"We show that the de Bruijn-Erd\\H{o}s condition for the error term in their improvement of Fekete's Lemma is not only sufficient but also necessary in the following strong sense. Suppose that given a sequence $0\\leq f(1)\\leq f(2)\\leq f(3)\\leq \\dots $ such that \\begin{equation}\\sum_{ n=1}^{\\infty} f(n)/n^2 = \\infty.\n  \\end{equation} Then, there exists a sequence $\\{b(n)\\}_{n=1,2,\\dots}$ satisfying \\begin{equation}\\label{eq1} b(n+m) \\leq b(n) + b(m) + f(n+m)\n  \\end{equation} such that the sequence of slopes $\\{ b(n)/n\\}_{n=1,2,\\dots}$ takes every rational number.\n  When the series is bounded we i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11723","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":""},"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"}