Probabilistic methods in combinatorial analysis
著者
書誌事項
Probabilistic methods in combinatorial analysis
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 56）
Cambridge University Press, 2010
- : pbk
- タイトル別名
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Вероятностные методы в комбинаторном анализе
Veroi︠a︡tnostnye metody v kombinatornom analize
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注記
Includes bibliographical references (p. [237]-243) and index
内容説明・目次
内容説明
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.
目次
- 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.
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