The EGZ-constant and short zero-sum sequences over finite abelian groups

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• 作者：Weidong Gao ; ^{wdgao1963@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; Dongchun Han ^{han-qingfeng@163.com" class="auth_mail" title="E-mail the corresponding author} ; Hanbin Zhang ^{nkuzhanghanbin@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Zero-sum sequence ; Short zero-sum sequence ; Davenport constant ; EGZ-constant
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：162
• 期：Complete
• 页码：601-613
• 全文大小：308 K

文摘

Let G   be an additive finite abelian group with exponent g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si1.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=ae3fec66ea8e3cd3e3de4244bea5a3ed" title="Click to view the MathML source">exp⁡(G)gif" overflow="scroll">exp⁡(G). Let g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si2.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=5a8fcf810daab4f87843c147ebc0b651" title="Click to view the MathML source">η(G)gif" overflow="scroll">η(G) be the smallest integer t such that every sequence of length t   has a nonempty zero-sum subsequence of length at most g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si1.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=ae3fec66ea8e3cd3e3de4244bea5a3ed" title="Click to view the MathML source">exp⁡(G)gif" overflow="scroll">exp⁡(G). Let g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si3.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=d0193b270d6dfd382cda803d919c9f0e" title="Click to view the MathML source">s(G)gif" overflow="scroll">s(G) be the EGZ-constant of G, which is defined as the smallest integer t such that every sequence of length t   has a zero-sum subsequence of length g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si1.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=ae3fec66ea8e3cd3e3de4244bea5a3ed" title="Click to view the MathML source">exp⁡(G)gif" overflow="scroll">exp⁡(G). Let p   be an odd prime. We determine g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si2.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=5a8fcf810daab4f87843c147ebc0b651" title="Click to view the MathML source">η(G)gif" overflow="scroll">η(G) for some groups G   with g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si27.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=991577ffd7420f84afd40308c0034452" title="Click to view the MathML source">D(G)≤2exp⁡(G)−1gif" overflow="scroll">D(G)≤2exp⁡(G)−1, including the p-groups of rank three and the p  -groups g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si5.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=7280bfe83def86262cc4904da41feccf">g class="imgLazyJSB inlineImage" height="18" width="136" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022314X15003327-si5.gif">gif" overflow="scroll">G=Cexp⁡(G)⊕Cpmr. We also determine g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si3.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=d0193b270d6dfd382cda803d919c9f0e" title="Click to view the MathML source">s(G)gif" overflow="scroll">s(G) for the groups G   above with more larger exponent than g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si7.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=585ad9a6d4945fcca21f1ba45859923c" title="Click to view the MathML source">D(G)gif" overflow="scroll">D(G), which confirms a conjecture by Schmid and Zhuang from 2010, where g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X15003327&_mathId=si7.gif&_user=111111111&_pii=S0022314X15003327&_rdoc=1&_issn=0022314X&md5=585ad9a6d4945fcca21f1ba45859923c" title="Click to view the MathML source">D(G)gif" overflow="scroll">D(G) denotes the Davenport constant of G.

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