On the existence of zero-sum subsequences of distinct lengths

Benjamin Girard
2012 Rocky Mountain Journal of Mathematics  
In this paper, we obtain a characterization of short normal sequences over a finite Abelian p-group, thus answering positively a conjecture of Gao for a variety of such groups. Our main result is deduced from a theorem of Alon, Friedland and Kalai, originally proved so as to study the existence of regular subgraphs in almost regular graphs. In the special case of elementary p-groups, Gao's conjecture is solved using Alon's Combinatorial Nullstellensatz. To conclude, we show that, assuming every
more » ... hat, assuming every integer satisfies Property B, this conjecture holds in the case of finite Abelian groups of rank two.
doi:10.1216/rmj-2012-42-2-583 fatcat:r54wrsuz65gohd2sjoxt4mjeti