{"paper":{"title":"Sharp bound on the number of maximal sum-free subsets of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Andrew Treglown, Hong Liu, J\\'ozsef Balogh, Maryam Sharifzadeh","submitted_at":"2015-02-26T15:51:49Z","abstract_excerpt":"Cameron and Erd\\H{o}s asked whether the number of \\emph{maximal} sum-free sets in $\\{1, \\dots , n\\}$ is much smaller than the number of sum-free sets. In the same paper they gave a lower bound of $2^{\\lfloor n/4 \\rfloor }$ for the number of maximal sum-free sets. Here, we prove the following: For each $1\\leq i \\leq 4$, there is a constant $C_i$ such that, given any $n\\equiv i \\mod 4$, $\\{1, \\dots , n\\}$ contains $(C_i+o(1)) 2^{n/4}$ maximal sum-free sets. Our proof makes use of container and removal lemmas of Green, a structural result of Deshouillers, Freiman, S\\'os and Temkin and a recent bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07605","kind":"arxiv","version":2},"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"}