Probabilistic Methods in Combinatorial Analysis

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Hardcover | 14 July 1997

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Hardcover
260 Pages

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23.39 x 15.6 x 1.6

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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.

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Preface
Preface to the English edition
Introduction
Relevant elements from probability theory
Combinatorial properties or random nonnegative matrices
Probabilistic problems in the general combinatorial scheme
Random partitions of sets
Random permutations
Random graphs and random mappings
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

Probabilistic Methods in Combinatorial Analysis

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Hardcover

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