The restricted sumsets in finite abelian groups

2024/03/06 by Du, Shanshan, Pan, Hao
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2403.03549

Abstract

Suppose that k≥ 2 and A is a non-empty subset of a finite abelian group G with |G|>1. Then the cardinality of the restricted sumset k^\wedge A:=\a₁+⋯+a_k: a₁,…,a_k∈ A, a_i≠ a_j for i≠ j\ is at least min\p(G), k|A|-k²+1\, where p(G) denotes the least prime divisor of |G|.

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