Combinatorial Methods in Discrete Mathematics

ISBN-13: 9780521455138 / Angielski / Twarda / 1996 / 324 str.

V. Sachkov; Vladimir Nikolaevich Sachkov

Opis

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.

Recenzje

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

Spis treści

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.