{"paper":{"title":"On an inverse problem for restricted sumsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Xin-Qi Luo, Zhi-Wei Sun","submitted_at":"2023-05-19T10:21:19Z","abstract_excerpt":"Let $n$ be a positive integer, and let $A$ be a set of $k\\ge 2n-1$ integers. For the restricted sumset $$ S_n(A)=\\{a_1+\\cdots +a_n:\\ a_1,\\ldots,a_n\\in A,\\ \\text{and}\\ a_i^2\\neq a_j^2\\ \\text{for} \\ 1\\le i<j\\le n\\}, $$ by a 2002 result of Liu and Sun we have $$|S_n(A)|\\ge (k-1)n-\\frac 32n(n-1)+1.$$ In this paper, we determine the structure of $A$ when the lower bound is attained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.11574","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.11574/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}