A first course in combinatorial mathematics
著者
書誌事項
A first course in combinatorial mathematics
（Oxford applied mathematics and computing science series）
Clarendon Press , Oxford University Press, 1989
2nd ed.
- : pbk
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注記
Bibliography: p. 131-132
Includes index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198596738
内容説明
The spirit and aim of this book is to present a compact introduction to the basic combinatorial tools - such as recurrence relations, generating functions, incidence matrices, and the inclusion-exclusion principle - that will give the reader a flavour of the distinctive characteristics of this attractive and increasingly important branch of mathematics.
A studly of block designs is followed by a brief mention of applications to coding theory. In this new edition, Steiner triple systems are constructed and S(5,8,24) is obtained via the Golay code of length 24. The final chapter combines together the three combinatorial structures of the Leech lattice, the Golay codes, and Steiner systems. Also in this edition, an application of the marriage theorem to score sequences of tournaments has been included.
目次
- Introduction to basic ideas
- Selections and binomial coefficients
- Pairing problems
- Recurrence
- The inclusion-exclusion principle
- Block designs and error-correcting codes
- Steiner systems, sphere packings, and the Golay code
- Solutions to exercises
- Bibliography
- Index
- 巻冊次
-
ISBN 9780198596745
内容説明
This introduction to the basic combinatorial tools, such as recurrence relations, generating functions, incidence matrices and the inclusion-exclusion principle, has been designed to give readers a flavour of the distinctive characteristics of this branch of mathematics. The text contains a study of block designs, which is followed by a brief mention of their application to coding theory. In this new edition, Steiner triple systems are constructed and the three combinatorial structures of the Leech lattice, the Golay codes and Steiner systems are examined. The edition also includes an application of the marriage theorem to score sequences of tournaments.
目次
- Selections and binomial coefficients
- pairings problems
- recurrence
- the inclusion-exclusion principle
- block designs and error-correcting codes
- Steiner systems, sphere packings and the Golay code.
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