{"paper":{"title":"Direct and Inverse Theorems on Signed Sumsets of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jagannath Bhanja, Ram Krishna Pandey","submitted_at":"2018-10-05T13:32:12Z","abstract_excerpt":"Let $G$ be an additive abelian group and $h$ be a positive integer. For a nonempty finite subset $A=\\{a_0, a_1,\\ldots, a_{k-1}\\}$ of $G$, we let \\[h_{\\underline{+}}A:=\\{\\Sigma_{i=0}^{k-1}\\lambda_{i} a_{i}: (\\lambda_{0}, \\ldots, \\lambda_{k-1}) \\in \\mathbb{Z}^{k},~ \\Sigma_{i=0}^{k-1}|\\lambda_{i}|=h \\},\\] be the {\\it signed sumset} of $A$.\n  The {\\it direct problem} for the signed sumset $h_{\\underline{+}}A$ is to find a nontrivial lower bound for $|h_{\\underline{+}}A|$ in terms of $|A|$. The {\\it inverse problem} for $h_{\\underline{+}}A$ is to determine the structure of the finite set $A$ for wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02673","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"}