This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the study of random graphs and permutations reduces the combinatorial problems to classical problems of probability theory on the summation of independent random variables. He concentrates on research by Russian mathematicians, including a discussion of equations containing an unknown permutation and a presentation of techniques for solving systems of random linear equations in finite fields. These results will interest specialists in combinatorics and probability theory and will also be useful in applied areas of probabilistic combinatorics such as communication theory, cryptology, and mathematical genetics.

• Presents many important Russian results in English • Unified approach shows connections between combinatorial problems, graph theory, and classical probability theory

### Contents

Preface; 1. The generalized scheme of allocation and the components of random graphs; 2. Evolution of random graphs; 3. Systems of random linear equations in GF(2); 4. Random permutations; 5. Equations containing an unknown permutation; Bibliography; Index.

### Review

Review of the hardback: 'Many of the results appear here for the first time in an English translation. The book is therefore to be welcomed for bringing this material to a wider audience.' W. T. Gowers, Bulletin of the London Mathematical Society