Combinatorial Methods in Discrete Mathematics

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Cambridge University Press, Jan 11, 1996 - Mathematics - 306 pages
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Discrete mathematics is an important tool for the investigation of various models of functioning of technical devices, especially in the field of cybernetics. Here the author presents some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. Professor Sachkov's aim is to focus attention on results that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived. Professor Sachkov begins with a discussion of block designs and Latin squares before proceeding to treat transversals, devoting much attention to enumerative problems. The main role in these problems is played by generating functions, considered in Chapter 4. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book for graduate students and professionals that describes many ideas not previously available in English; the author has updated the text and references where appropriate.
 

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Contents

1 Combinatorial configurations
1
2 Transversals and permanents
49
3 Generating functions
102
4 Graphs and mappings
165
5 The general combinatorial scheme
209
6 Polyas theorem and its applications
272
Bibliography
295
Index
303
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