Combinatorial Methods in Discrete Mathematics

A 1996 account of some complex problems of discrete mathematics in a simple and unified form.

Vladimir N. Sachkov (Author), V. Kolchin (Translated by)

9780521455138, Cambridge University Press

Hardback, published 11 January 1996

324 pages
24.1 x 16.2 x 2.3 cm, 0.631 kg

Review of the hardback: ' … 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.' I. Anderson, Bulletin of the Edinburgh Mathematical Society

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.

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.

Subject Areas: Combinatorics & graph theory [PBV]