Author:
Hu Yuting,Peng Jiangtao,Wang Mingrui
Abstract
<abstract><p>Let $ G $ be a finite abelian group with exponent $ \exp(G) $ and $ S $ be a sequence with elements of $ G $. We say $ S $ is a zero-sum sequence if the sum of the elements in $ S $ is the zero element of $ G $. For a positive integer $ t $, let $ \mathtt{s}_{t\exp(G)}(G) $ (respectively, $ \mathtt{s}'_{t\exp(G)}(G) $) denote the smallest integer $ \ell $ such that every sequence (respectively, zero-sum sequence) $ S $ over $ G $ with $ |S|\geq \ell $ contains a zero-sum subsequence of length $ t\exp(G) $. The invariant $ \mathtt{s}_{t\exp(G)}(G) $ (respectively, $ \mathtt{s}'_{t\exp(G)}(G) $) is called the Generalized Erdős-Ginzburg-Ziv constant (respectively, Modified Erdős-Ginzburg-Ziv constant) of $ G $. In this paper, we discuss the relationship between Generalized Erdős-Ginzburg-Ziv constant and Modified Erdős-Ginzburg-Ziv constant, and determine $ \mathtt{s}'_{t\exp(G)}(G) $ for some finite abelian groups.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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