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  3. Probabilistic Methods in Combinatorial Analysis
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1997
Online ISBN:
9780511666193
DOI:
https://doi.org/10.1017/CBO9780511666193
Subjects:
Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding
Series:
Encyclopedia of Mathematics and its Applications (56)
Information

Book description

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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