{"paper":{"title":"Upper bounds for $B_h[g]$-sets with small $h$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Craig Timmons","submitted_at":"2016-04-03T17:38:48Z","abstract_excerpt":"For $g \\geq 2$ and $h \\geq 3$, we give small improvements on the maximum size of a $B_h[g]$-set contained in the interval $\\{1,2, \\dots , N \\}$. In particular, we show that a $B_3[g]$-set in $\\{1,2, \\dots , N \\}$ has at most $(14.3 g N)^{1/3}$ elements. The previously best known bound was $(16 gN)^{1/3}$ proved by Cilleruelo, Ruzsa, and Trujillo. We also introduce a related optimization problem that may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00661","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"}