{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:6Y2QQD5BJVMYCVYASCFP6U5NWX","short_pith_number":"pith:6Y2QQD5B","schema_version":"1.0","canonical_sha256":"f635080fa14d59815700908aff53adb5cc8172f964d03febdae54fe4f1997972","source":{"kind":"arxiv","id":"math/0610893","version":1},"attestation_state":"computed","paper":{"title":"On Snevily's conjecture and restricted sumsets","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Zhi-Wei Sun","submitted_at":"2006-10-29T14:01:46Z","abstract_excerpt":"Let G be an additive abelian group whose finite subgroups are all cyclic. Let A_1,...,A_n (n>1) be finite subsets of G with cardinality k>0, and let b_1,...,b_n be pairwise distinct elements of G with odd order. We show that for every positive integer m\\leq (k-1)/(n-1) there are more than (k-1)n-(m+1)n(n-1)/2 sets {a_1,...,a_n} such that a_1\\in A_1,..., a_n\\in A_n, and both a_i\\not=a_j and ma_i+b_i\\not=ma_j+b_j (or both ma_i\\not=ma_j and a_i+b_i\\not=a_j+b_j) for all 1\\leq i1) be finite subsets of G with cardinality k>0, and let b_1,...,b_n be pairwise distinct elements of G with odd order. We show that for every positive integer m\\leq (k-1)/(n-1) there are more than (k-1)n-(m+1)n(n-1)/2 sets {a_1,...,a_n} such that a_1\\in A_1,..., a_n\\in A_n, and both a_i\\not=a_j and ma_i+b_i\\not=ma_j+b_j (or both ma_i\\not=ma_j and a_i+b_i\\not=a_j+b_j) for all 1\\leq i