{"paper":{"title":"Restricted-sum-dominant sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Raj Kumar Mistri, R. Thangadurai","submitted_at":"2017-12-26T10:13:01Z","abstract_excerpt":"Let $A$ be a nonempty finite subset of an additive abelian group $G$. Define $A + A := \\{a + b : a, b \\in A\\}$ and $A \\dotplus A := \\{a + b : a, b \\in A~\\text{and}~ a \\neq b\\}$. The set $A$ is called a {\\em sum-dominant (SD) set} if $|A + A| > |A - A|$, and it is called a {\\em restricted sum-domonant (RSD) set} if $|A \\dotplus A| > |A - A|$. In this paper, we prove that for infinitely many positive integers $k$, there are infinitely many RSD sets of integers of cardinality $k$. We also provide an explicit construction of infinite sequence of RSD sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09226","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"}