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On an inverse problem of Erdős, Kleitman, and Lemke
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2020-08-25 , DOI: 10.1016/j.jcta.2020.105323
Qinghai Zhong

Let (G,1G) be a finite group and let S=g1g be a nonempty sequence over G. We say S is a tiny product-one sequence if its terms can be ordered such that their product equals 1G and i=11ord(gi)1. Let ti(G) be the smallest integer t such that every sequence S over G with |S|t has a tiny product-one subsequence. The direct problem is to obtain the exact value of ti(G), while the inverse problem is to characterize the structure of long sequences over G which have no tiny product-one subsequence. In this paper, we consider the inverse problem for cyclic groups and we also study both direct and inverse problems for dihedral groups and dicyclic groups.



中文翻译:

关于Erdős,Kleitman和Lemke的反问题

G1个G 成为一个有限的群体,让 小号=G1个GG上的非空序列。我们说S是一个很小的乘积序列,如果可以对它们的项进行排序以使它们的乘积等于1个G一世=1个1个奥德G一世1个。让tiG是最小的整数,使得每个序列š超过ģ|小号|Ť有一个很小的乘积一子序列 直接的问题是要获得tiG,而反问题是表征G上没有微小乘积一子序列的长序列的结构。在本文中,我们考虑了环状群的逆问题,同时研究了二面体群和二环群的正反问题。

更新日期:2020-08-25
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