{"paper":{"title":"Generalized More Sums Than Differences Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Geoffrey Iyer, Liyang Zhang, Oleg Lazarev, Steven J. Miller","submitted_at":"2011-08-23T05:46:04Z","abstract_excerpt":"A More Sums Than Differences (MSTD, or sum-dominant) set is a finite set $A\\subset \\mathbb{Z}$ such that $|A+A|<|A-A|$. Though it was believed that the percentage of subsets of $\\{0,...,n\\}$ that are sum-dominant tends to zero, in 2006 Martin and O'Bryant \\cite{MO} proved a positive percentage are sum-dominant. We generalize their result to the many different ways of taking sums and differences of a set. We prove that $|\\epsilon_1A+...+\\epsilon_kA|>|\\delta_1A+...+\\delta_kA|$ a positive percent of the time for all nontrivial choices of $\\epsilon_j,\\delta_j\\in \\{-1,1\\}$. Previous approaches prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4500","kind":"arxiv","version":3},"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"}