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Author: Barry A. Bunin
Publisher:
ISBN: 9780121413453
Category :
Languages : en
Pages :
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Book Description
Author: Barry A. Bunin
Publisher:
ISBN: 9780121413453
Category :
Languages : en
Pages :
Get Book Here
Book Description
Author: Bruce E. Sagan
Publisher: American Mathematical Soc.
ISBN: 1470460327
Category : Education
Languages : en
Pages : 304
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Book Description
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
Author: George Polya
Publisher: Springer Science & Business Media
ISBN: 1475711018
Category : Science
Languages : en
Pages : 202
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Book Description
In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.
Author: Xueliang Li
Publisher: Springer Science & Business Media
ISBN: 1461431190
Category : Mathematics
Languages : en
Pages : 108
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Book Description
Rainbow connections are natural combinatorial measures that are used in applications to secure the transfer of classified information between agencies in communication networks. Rainbow Connections of Graphs covers this new and emerging topic in graph theory and brings together a majority of the results that deal with the concept of rainbow connections, first introduced by Chartrand et al. in 2006. The authors begin with an introduction to rainbow connectedness, rainbow coloring, and rainbow connection number. The work is organized into the following categories, computation of the exact values of the rainbow connection numbers for some special graphs, algorithms and complexity analysis, upper bounds in terms of other graph parameters, rainbow connection for dense and sparse graphs, for some graph classes and graph products, rainbow k-connectivity and k-rainbow index, and, rainbow vertex-connection number. Rainbow Connections of Graphs appeals to researchers and graduate students in the field of graph theory. Conjectures, open problems and questions are given throughout the text with the hope for motivating young graph theorists and graduate students to do further study in this subject.
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: Kenneth P. Bogart
Publisher: Harcourt Brace College Publishers
ISBN:
Category : Computers
Languages : en
Pages : 648
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Book Description
Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.
Author: Barry A. Bunin
Publisher: Elsevier
ISBN: 0080542409
Category : Science
Languages : en
Pages : 341
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Book Description
With the explosion of combinatorial solid-phase methods, access to information has become one of the main barriers facing a synthetic chemist who is contemplating a combinatorial approach to a medicinal chemistry problem. The Combinatorial Index is an answer to that problem. This compendium of methods from the primary literature provides quick and convenient access to reliable synthetic transformations as well as information on linkers and analytical methods. Each synthetic procedure is preceded by a section entitled"Points of Interest,"which highlights the strengths and weaknesses of the various studies. The index also covers the use of solution-based synthesis for the generation of molecular diversity. Organized for rapid retrieval of published information on classes of synthetic transformations, linkers, and analytical methods Serves as a laboratory manual for bench chemists Includes a chapter on linkers to assist in choice of linking strategy Discusses strengths and limitations of the various methods Contains a structural index showing functional group transformations in solid-phase synthesis
Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 1584887443
Category : Computers
Languages : en
Pages : 664
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Book Description
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 combinat
Author: Jiri Herman
Publisher: Springer Science & Business Media
ISBN: 1475739257
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.
Author: John Harris
Publisher: Springer Science & Business Media
ISBN: 0387797114
Category : Mathematics
Languages : en
Pages : 392
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Book Description
These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
