【摘要】：零和理論是組合數(shù)論的重要組成部分,其主要研究有限Abe1加法群中序列的組合性質(zhì).而與序列的index相關(guān)的零和問題又是近幾年來零和領(lǐng)域研究的熱點(diǎn).零和序列是零和問題研究的主要對象.與零和序列相關(guān)的組合常數(shù)的確定問題被稱為直接零和問題;與之對應(yīng)的極值序列,如零和自由序列與n-零和自由序列結(jié)構(gòu)刻畫是零和問題的反問題.本文從反零和問題的角度,考慮n階循環(huán)群Cn上與序列的index相關(guān)的零和問題.本文工作主要有以下幾個(gè)方面:1.介紹零和問題的研究背景以及對序列index相關(guān)零和問題研究的進(jìn)展;說明本文中常用符號的含義;闡述加性數(shù)論以及群論的相關(guān)定理和一些基本概念;以及給出本文的結(jié)構(gòu)安排.2.綜述有限循環(huán)群Cn上與最小零和序列相關(guān)的組合常數(shù)l(Cn)的確定以及零和序列和零和自由序列結(jié)構(gòu)刻畫問題.考慮了長度大于(n+2)/3的零和自由序列S的結(jié)構(gòu)特點(diǎn).3.總結(jié)循環(huán)群Cn上的n-零和自由序列的結(jié)構(gòu)刻畫問題.基于長度大于(3n)/2-1的n-零和自由序列的結(jié)構(gòu)刻畫,結(jié)合前人的工作,本文對長度大于(4n)/3-1的n-零和自由序列的結(jié)構(gòu)的部分情況進(jìn)行刻畫.
[Abstract]:The theory of zero sum is an important part of combinatorial number theory. It mainly studies the combinatorial properties of sequences in finite Abe1 additive groups. The zero sum problem related to the index of sequences is a hot topic in the field of zero sum in recent years. Zero sum sequence is the main research object of zero sum problem. The problem of determining combinatorial constants related to zero-sum sequences is called direct zero-sum problem, and the corresponding extremal sequences, such as zero-sum free sequences and nzero-sum free sequences structure characterization is the inverse problem of zero-sum problem. In this paper, from the point of view of anti-zero sum problem, we consider the zero-sum problem related to the index of sequences on the n-order cyclic group Cn. The main work of this paper is as follows: 1. This paper introduces the research background of zero-sum problem and the research progress of sequence index correlation zero-sum problem, explains the meaning of common symbols in this paper, expounds the related theorems and some basic concepts of additive number theory and group theory. And give the structure of this paper. 2. This paper reviews the determination of the combination constant l (Cn) related to the minimum zero-sum sequence on the finite cyclic group Cn and the characterization of the zero-sum sequence and the zero-sum free sequence structure. The structural characteristics of zero sum free sequence S with length greater than (N2) / 3 are considered. The structure characterization of n- zero sum free sequences on cyclic group Cn is summarized. Based on the structural characterization of nzero-sum free sequences with length greater than (3n) / 2-1 and previous work, this paper describes some cases of nzero-sum free sequences with length greater than (4n) / 3-1.
【學(xué)位授予單位】：大連海事大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O156

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本文編號：2392066