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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.12044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-10-21T15:38:12Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"c7eb4da523d2b35e0dc7ac5a70bfa487f20a7c71c9fae186e3ad4416c871b6a8","abstract_canon_sha256":"6a054ffb7683b2d11bc7836b7d7cfd31a12c47e8fe732ee14cfd59a944d008f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:09:08.512692Z","signature_b64":"RbQzITSWAnaUe75mbawQ06/z3bHFXKXGEjPfU8/xt+k8GwQeZZjdL/nSgdwBABU5Wn85s94hPV7IXXiBqdeADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13053416935c24c1420a01c3f741527daa5517f4ca33b14b19272b92d3d1a359","last_reissued_at":"2026-07-05T05:09:08.512329Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:09:08.512329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $|A_1|=\\cdots=|A_n|\\ge2$. 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