On the generalized restricted sumsets in abelian groups

2016/09/09 by Du, Shanshan, Pan, Hao
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.02833

Abstract

Suppose that A, B and S are non-empty subsets of a finite abelian group G. Then the generalized restricted sumset A\stackrelS+B:=\a+b: a∈ A, b∈ B, a-b\not∈ S\ contains at least min\|A|+|B|-3|S|,p(G)\ elements, where p(G) is the least prime factor of |G|. Further, we also have |A\stackrelS+B|≥ min\|A|+|B|-|S|-2,p(G)\, provided that both |A| and |B| are large with respect to |S|.

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