CAJ | 학술논문

设G是指数为n的有限Abel群,用s(G)表示满足下面条件的最小正整数t:元素在G中且长不小于t的序列中都包含长为n的零和子序列.在实际研究中,我们通常考虑s(Zkn). 但是除了n=2t外,s(Zkn)很难确定,至今我们只确定了s(Z33)和s(Z43).而s(Z36)是当n是合数,且k≥3时最简单的没确定的情况.为了研究具体的s(Z36)值,本文刻划了由Z36中元素构成的长为41或42的序列中不包含长为6的零和子序列的结构.
설G시지수위n적유한Abel군,용s(G)표시만족하면조건적최소정정수t:원소재G중차장불소우t적서렬중도포함장위n적령화자서렬.재실제연구중,아문통상고필s(Zkn). 단시제료n=2t외,s(Zkn)흔난학정,지금아문지학정료s(Z33)화s(Z43).이s(Z36)시당n시합수,차k≥3시최간단적몰학정적정황.위료연구구체적s(Z36)치,본문각화료유Z36중원소구성적장위41혹42적서렬중불포함장위6적령화자서렬적결구.
Let G be a finite abelian group of exponent n.We define s(G) as the smallest integer t so that every sequence of t elements in G contains a zero-sum subsequence of length n.s(G) is usually studied in group of the form G=Zkn.Finding the exact values of s(Zkn) seems to be a very difficult problem.Till now,we only know the exact value of s(Zk2t),s(Z33) and s(Z43).Let n be a composite number,and k≥3,then s(Z36) is the simplest undetermined case.Suppose S is a sequence of elements in Z36 and S contains no zero-sum subsequence of length .In this paper,we showed the structure of S.