Probabilistic Methods in Combinatorial Analysis (Encyclopedia of Mathematics and its Applications)

This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied 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 define 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 important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.

This work explores the role of probabilistic methods for solving combinatorial problems. These methods not only provide the means of efficiently using ideas from probability theory but also let us use the powerful technique of limit theorems. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods.This is 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.