{"paper":{"title":"On two new kinds of restricted sumsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Han Wang, Zhi-Wei Sun","submitted_at":"2022-10-21T15:38:12Z","abstract_excerpt":"Let $A_1,\\ldots,A_n$ be finite subsets of an additive abelian group $G$ with $|A_1|=\\cdots=|A_n|\\ge2$. Concerning the two new kinds of restricted sumsets $$L(A_1,\\ldots,A_n)=\\{a_1+\\cdots+a_n:\\ a_1\\in A_1,\\ldots,a_n\\in A_n,\\ \\text{and}\\ a_i\\not=a_{i+1} \\ \\text{for}\\ 1\\le i<n\\}$$ and $$C(A_1,\\ldots,A_n)=\\{a_1+\\cdots+a_n:\\ a_i\\in A_i\\ (1\\le i\\le n),\\ \\text{and}\\ a_i\\not=a_{i+1} \\ \\text{for}\\ 1\\le i<n,\\ \\text{and}\\ a_n\\not=a_1\\}$$ recently introduced by the second author, when $G$ is the additive group of a field we obtain lower bounds for $|L(A_1,\\ldots,A_n)|$ and $|C(A_1,\\ldots,A_n)|$ via the po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.12044","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/2210.12044/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"}