科研之友
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摘要
For a finite abelian group G, the generalized Erdős–Ginzburg–Ziv constant sk(G) is the smallest m such that a sequence of m elements in G always contains a k-element subsequence which sums to zero. If n=exp(G) is the exponent of G, the previously best known bounds for skn(Cnr) were linear in n and r when k≥2. Via a probabilistic argument, we produce the exponential lower bound s2n(Cnr)>n2[1.25+o(1)]rfor n>0. For the general case, we show skn(Cnr)>kn4(1+1ek+1+o(1))r.
