{"paper":{"title":"Sets Characterized by Missing Sums and Differences in Dilating Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Archit Kulkarni, David Moon, Jake Wellens, James Wilcox, Steven J. Miller, Thao Do","submitted_at":"2014-06-09T02:28:20Z","abstract_excerpt":"A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\\{0,\\dots,n\\}$ is bounded below by a positive constant as $n\\to\\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\\in\\mathbb{N}_0$, the proportion $\\rho^{s,d}_n$ of subsets of $\\{0,\\dots,n\\}$ that are missing exactly $s$ sums in $\\{0,\\dots,2n\\}$ and exactly $2d$ differences"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2052","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"}