Combinatorial Methods with Computer Applications

Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 1584887443
Format: PDF
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Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Algebraic and Combinatorial Methods in Operations Research

Author: R.E. Burkard
Publisher: Elsevier
ISBN: 9780080872063
Format: PDF, ePub, Mobi
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For the first time, this book unites different algebraic approaches for discrete optimization and operations research. The presentation of some fundamental directions of this new fast developing area shows the wide range of its applicability. Specifically, the book contains contributions in the following fields: semigroup and semiring theory applied to combinatorial and integer programming, network flow theory in ordered algebraic structures, extremal optimization problems, decomposition principles for discrete structures, Boolean methods in graph theory and applications.

Probabilistic Methods in Combinatorial Analysis

Author: Vladimir Nikolaevich Sachkov
Publisher: Cambridge University Press
ISBN: 9780521455121
Format: PDF, Docs
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This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.

Combinatorial Methods in Discrete Distributions

Author: Charalambos A. Charalambides
Publisher: John Wiley & Sons
ISBN: 0471733172
Format: PDF, ePub, Mobi
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A unique approach illustrating discrete distribution theory throughcombinatorial methods This book provides a unique approach by presenting combinatorialmethods in tandem with discrete distribution theory. This method,particular to discreteness, allows readers to gain a deeperunderstanding of theory by using applications to solve problems.The author makes extensive use of the reduction approach toconditional distributions of independent random occupancy numbers,and provides excellent studies of occupancy and sequentialoccupancy distributions, convolutions of truncated discretedistributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with abrief presentation of set theory followed by basic countingprinciples. Fundamental principles of combinatorics, finitedifferences, and discrete probability are included to give readersthe necessary foundation to the topics presented in the text. A thorough examination of the field is provided andfeatures: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complextheory and discovering how theory can be applied to solve practicalproblems. An appendix with hints and answers to the exercises helpsreaders work through the more complex sections. Reference notes areprovided at the end of each chapter, and an extensive bibliographyoffers readers a resource for additional information on specializedtopics.

Introductory Discrete Mathematics

Author: V. K . Balakrishnan
Publisher: Courier Corporation
ISBN: 0486140385
Format: PDF
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This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

Discrete Mathematics

Author: László Lovász
Publisher: Springer Science & Business Media
ISBN: 0387217770
Format: PDF, Docs
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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Combinatorial Methods in Topology and Algebra

Author: Bruno Benedetti
Publisher: Springer
ISBN: 3319201557
Format: PDF, ePub, Mobi
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Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.