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引言 本文对“组合拓扑方法在图论和拟阵理论中的一些应用”一文作些补充,介绍组合拓扑方法在图的平面性判定准则,图和n维复形的连通剖分和Hadwiger猜想等方面的一些应用. 相似文献
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离散事件动态系统研究中图论方法的某些应用 总被引:1,自引:0,他引:1
因为许多离散生产过程都可以用离散事件系统描述,所以离散事件动态系统有很强的实用背景,例如柔性制造系统,因此,受到国内外的广泛注意和重视,进行深入研究,已获得一些很重要的理论结果.本文试图用图论的观点和方法,对离散事件动态系统的某些重要结果予以注释和新的证明,并探讨图论在该领域研究中的进一步应用. 相似文献
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母函数是将复杂计数问题简单化的一个工具,利用母函数来处理中学数学中的某些组合问题,可操作性强,学生容易理解.本文先介绍母函数的基本知识,然后用母函数理解一些经典组合问题,再介绍母函数在解决某些复杂计数问题中的应用. 相似文献
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谈谈与图有关的几种复形的同调群 总被引:2,自引:0,他引:2
我们从组合拓扑方法在图论的应用中,着重介绍与图有关的几种复形的近期研究动态,论述其中一些基础性的问题,并提出一些可供研究的新问题。 相似文献
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我们证明了有限域上的一类方程组解的个数与图的顶点着色数有密切关系,而这又对许多着色问题的产生了许多应用。另外,我们也用图论的一些技巧解决了数论中一些问题。 相似文献
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一类可数离散半群上概率测度序列的组合收敛性 总被引:1,自引:0,他引:1
本文讨论具有单位元的可数离散半群上概率测度序列的组合收敛性,主要结果推广了有限群上的Maksimov定理,同时也蕴含了Center,Mukherjea等人的一些结论. 相似文献
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Vladimir I. Levenshtein Johannes Siemons 《Journal of Combinatorial Theory, Series A》2009,116(4):795-815
Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory which is also based on the consideration of metric balls of vertices, but which is distinct from the traditional packing and covering problems. This problem is motivated by applications in information transmission when redundancy of messages is not sufficient for their exact reconstruction, and applications in computational biology when one wishes to restore an evolutionary process. It can be defined as the reconstruction, or identification, of an unknown vertex in a given graph from a minimal number of vertices (erroneous or distorted patterns) in a metric ball of a given radius r around the unknown vertex. For this problem it is required to find minimum restrictions for such a reconstruction to be possible and also to find efficient reconstruction algorithms under such minimal restrictions.In this paper we define error graphs and investigate their basic properties. A particular class of error graphs occurs when the vertices of the graph are the elements of a group, and when the path metric is determined by a suitable set of group elements. These are the undirected Cayley graphs. Of particular interest is the transposition Cayley graph on the symmetric group which occurs in connection with the analysis of transpositional mutations in molecular biology [P.A. Pevzner, Computational Molecular Biology: An Algorithmic Approach, MIT Press, Cambridge, MA, 2000; D. Sankoff, N. El-Mabrouk, Genome rearrangement, in: T. Jiang, T. Smith, Y. Xu, M.Q. Zhang (Eds.), Current Topics in Computational Molecular Biology, MIT Press, 2002]. We obtain a complete solution of the above problems for the transposition Cayley graph on the symmetric group. 相似文献
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Reinhard Diestel 《Discrete Mathematics》2010,310(20):2750-29
This paper is the second of three parts of a comprehensive survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. The first two parts of the survey together provide a suitable entry point to this field for new readers; they are available in combined form from the ArXiv [20]. They are complemented by a third part [31], which looks at the theory from an algebraic-topological point of view.The topological approach indicated above has made it possible to extend to locally finite graphs many classical theorems of finite graph theory that do not extend verbatim. This second part of the survey concentrates on these applications, many of which solve problems or extend earlier work of Thomassen on infinite graphs. Numerous new problems are suggested. 相似文献
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A Guichardet 《Journal of multivariate analysis》1973,3(3):249-261
In recent years, applications of cohomology theory to some aspects of probability theory have been found useful. In this paper, such applications are discussed for a determination of infinitely divisible positive definite functions on topological groups. This theory can be viewed as a new method for determining the class of such characteristic functions which includes the classical Leavy-Khintchine representation formula for the groups Rn. 相似文献
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S. Pirzada 《PAMM》2007,7(1):2070013-2070013
Graph theory is rapidly moving into the mainstream of mathematics mainly because of its applications in diverse fields. In this paper, we discuss certain ways of applying graph theoretical techniques to solve various problems and present the review of some of the applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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本文中我们证明几个关于克希霍夫矩阵的新定理.在这些定理下,代数图论中Temperly,Kelmans,以及Fiedler提出的一些早期定理成为直接的推论. 相似文献
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Reinhard Diestel 《Discrete Mathematics》1992,100(1-3):313-327
This paper aims to give a brief introduction to a set of problems, old and new, concerned with one of the main and long-standing quests in infinite graph theory: how to represent the end structure of a given graph by that of a simpler subgraph, in particular a spanning tree. There has been a fair amount of activity in this field recently; we describe the latest results, as well as some of the new problems which these results suggest. 相似文献
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Russell Merris 《Linear and Multilinear Algebra》2013,61(3-4):211-224
Apart from some clarification of earlier work (Theorems 3 and 8), there is no new mathematics reported here. This is an expository article addressing some of the many applications of multilinear algebra, particularly those which touch upon the author's own work. Section 1 it. a brief introduction to the applicable ideas and techniques with special emphasis un group reprcscntaiiuns. Section 2 involves applications in quantum chemistry. Section 3 deals with combinatorial enumeration problems illustrated in the context of graph theory. The final section is devoted to generalized matrix tune-lions and some of their applications. 相似文献
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A. M. Raigorodskii 《Journal of Mathematical Sciences》2007,146(2):5723-5730
This work deals with some problems on the embeddings of finite geometric graphs into the random ones. In particular, we study here applications of the random graph theory to the Nelson-Erdös-Hadwiger problem on coloring spaces. 相似文献