Probabilistic Methods in Combinatorial Analysis

This 1997 book explores the role of probabilistic methods for solving combinatorial problems.

Vladimir N. Sachkov (Author), V. A. Vatutin (Translated by)

9780521172776, Cambridge University Press

Paperback, published 17 February 2011

258 pages
23.4 x 15.6 x 1.4 cm, 0.37 kg

This 1997 work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using such notions as characteristic and generating functions, the moment method and so on but also let us use the powerful technique of limit theorems. The basic objects under investigation are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these specify the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This was an important book, describing many ideas not previously available in English; the author has taken the chance to rewrite parts of the text and refresh the references where appropriate.

Preface
Preface to the English edition
Introduction
1. Relevant elements from probability theory
2. Combinatorial properties or random nonnegative matrices
3. Probabilistic problems in the general combinatorial scheme
4. Random partitions of sets
5. Random permutations
6. Random graphs and random mappings
Bibliography
Index.

Subject Areas: Combinatorics & graph theory [PBV]