Combinatorial Methods in Discrete Mathematics

Vladimir N. Sachkov, V. Kolchin

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English

Cambridge University Press
02 June 2011

Probability & statistics; Combinatorics & graph theory

Series: Encyclopedia of Mathematics and its Applications

Originally published in 1996, this is a presentation of some complex problems of discrete mathematics in a simple and unified form using an original, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones 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, which are considered in Chapter 3. The general combinatorial scheme is then introduced and in the last chapter Polya's enumerative theory is discussed. This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.

By: Vladimir N. Sachkov
Translated by: V. Kolchin
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 55
Dimensions: Height: 234mm, Width: 156mm, Spine: 17mm
Weight: 450g
ISBN: 9780521172769
ISBN 10: 0521172764
Series: Encyclopedia of Mathematics and its Applications
Pages: 322
Publication Date: 02 June 2011
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; Preface to the English edition; Introduction; 1. Combinatorial configurations; 2. Transversals and permanents; 3. Generating functions; 4. Graphs and mappings; 5. The general combinatorial scheme; 6. Polya's theorem and its applications; Bibliography; Index.

Reviews for Combinatorial Methods in Discrete Mathematics

' ... a very enjoyable and brisk introduction to the exciting fields of enumerative and probabilistic combinatorics'. ' ... for the serious student of generating functions and asymptotic techniques it provides an account of the work of Kolchin (who did the translation), the author and others which is not otherwise readily available in English.'