Article ID Journal Published Year Pages File Type
4648360 Discrete Mathematics 2009 5 Pages PDF
Abstract

In this paper, we prove that if AA and BB are subsets of a finite abelian group GG with |A|+|B|=|G|+L(G)|A|+|B|=|G|+L(G), then |A+ˆB|≥|G|−2, where L(G)=|{g:g∈G,2g=0}|L(G)=|{g:g∈G,2g=0}| andA+ˆB={a+b:a∈A,b∈B,a≠b}. In addition, we give a complete description of the subsets AA and BB of GG such that |A|+|B|=|G|+L(G)|A|+|B|=|G|+L(G) and A+ˆB≠G. Our results generalize the corresponding theorems of Gallardo et al. in cyclic group Z/nZZ/nZ [L. Gallardo, G. Grekos, L. Habsieger, et al., Restricted addition in Z/nZZ/nZ and an application to the Erdös–Ginzburg–Ziv problem, J. London Math. Soc. 65 (2) (2002) 513–523].

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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