組合せ解析における確率論的手法 Probabilistic Methods in Combinatorial Analysis (Encyclopedia of Mathematics and its Applications)

Sachkov, Vladimir N./ Vatutin, V. A. (TRN)

Cambridge University Press（2011/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 258 p.
• 言語 ENG
• 商品コード 9780521172776
• DDC分類 519.2

基本説明

New in paperback. Hardcover was published in 1997. Transl. by V. A. Vatutin.

Full 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.

Contents

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.