Remarks on Tiny Zero - Sum Sequences

نویسندگان

  • Yushuang Fan
  • Weidong Gao
  • Jiangtao Peng
  • Linlin Wang
  • Qinghai Zhong
چکیده

Let G be an additive finite abelian group with exponent exp(G). Let S = g1 · . . . · gl be a sequence over G and k(S) = ord(g1)+· · ·+ord(gl) be its cross number. Let η(G) (resp. t(G)) be the smallest integer t such that every sequence of t elements (repetition allowed) from G contains a non-empty zero-sum subsequence T of length |T | ≤ exp(G) (resp. k(T ) ≤ 1). It is easy to see that t(G) ≥ η(G) for all finite abelian groups G, and a previous result showed that for every positive integer r ≥ 4, there exist finite abelian groups of rank r such that t(G) > η(G). In this paper we provide the first example of groups G of rank three with t(G) > η(G). We also prove that t(G) = η(G) for G = C2 ⊕ C2p where p is a prime.

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تاریخ انتشار 2013