{"paper":{"title":"A geometric perspective on the MSTD question","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Carsten Peterson, Steven J. Miller","submitted_at":"2017-09-02T17:22:17Z","abstract_excerpt":"A more sums than differences (MSTD) set $A$ is a subset of $\\mathbb{Z}$ for which $|A+A| > |A-A|$. Martin and O'Bryant used probabilistic techniques to prove that a non-vanishing proportion of subsets of $\\{1, \\dots, n\\}$ are MSTD as $n \\to \\infty$. However, to date only a handful of explicit constructions of MSTD sets are known. We study finite collections of disjoint intervals on the real line, $\\mathbb{I}$, and explore the MSTD question for such sets, as well as the relation between such sets and MSTD subsets of $\\mathbb{Z}$. In particular we show that every finite subset of $\\mathbb{Z}$ ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00606","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"}