{"paper":{"title":"Fringe pairs in generalized MSTD sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hong Suh, Megumi Asada, Sarah Manski, Steven J. Miller","submitted_at":"2015-09-05T02:28:10Z","abstract_excerpt":"A More Sums Than Differences (MSTD) set is a set $A$ for which $|A+A|>|A-A|$. Martin and O'Bryant proved that the proportion of MSTD sets in $\\{0,1,\\dots,n\\}$ is bounded below by a positive number as $n$ goes to infinity. Iyer, Lazarev, Miller and Zhang introduced the notion of a generalized MSTD set, a set $A$ for which $|sA-dA|>|\\sigma A-\\delta A|$ for a prescribed $s+d=\\sigma+\\delta$. We offer efficient constructions of $k$-generational MSTD sets, sets $A$ where $A, A+A, \\dots, kA$ are all MSTD. We also offer an alternative proof that the proportion of sets $A$ for which $|sA-dA|-|\\sigma A-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01657","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"}