Probabilistic Methods in Combinatorial Analysis

ISBN-13: 9780521455121 / Angielski / Twarda / 1997 / 260 str.

V. N. Sachkov; V. N. Sachov; V. Sachkov

Opis

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.

Spis treści

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.