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More About This Textbook
Overview
This book considers one of the basic problems in discrete mathematics: given a collection of constraints, describe up to isomorphism all the objects that meet them. Only a handful of classification results for combinatorial objects are dated before the mid-20th century; indeed, it is through modern computers and recent developments in algorithms that this topic has flourished and matured. This book is the first comprehensive reference on combinatorial classification algorithms, with emphasis on both the general theory and application to central families of combinatorial objects, in particular, codes and designs.
The book will be of great interest to researchers and can be used as course material for graduate courses in both computer science and mathematics.
Editorial Reviews
From the Publisher
From the reviews:"The authors of this book have been responsible for some quite remarkable combinatorial enumeration results … . They are therefore well-qualified to provide this comprehensive survey of state-of-the-art algorithms for the classification of codes and designs. … Overall the book is a timely and authoritative work, and an extremely valuable reference for any researcher working in the field of combinatorial classification." (Peter B.Gibbons, Zentralblatt MATH, Vol. 1089 (15), 2006)
"For any researcher involved with combinatorial algorithms, this book is a must-have. It is absolutely essential for anyone doing enumeration algorithms on t-designs or codes. … This is one of the few useful books on combinatorial design algorithms. … Finally, the book contains (open) research problems sprinkled throughout, which should be useful for researchers … . It would make a good textbook for a senior undergraduate or a graduate course on computing in design and coding theory." (G. H. J. Van Rees and Pak Ching Li, Mathematical Reviews, Issue 2008 a)
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Table of Contents
1 Introduction.- 2 Graphs, Designs, and Codes.- 3 Representations and Isomorphism.- 4 Isomorph-Free Exhaustive Generation.- 5 Auxiliary Algorithms.- 6 Classification of Designs.- 7 Classification of Codes.- 8 Classification of Related Structures.- 9 Prescribing Automorphism Groups.- 10 Validity of Computational Results.- 11 Computational Complexity.- 12 Nonexistence of Projective Planes of Order 10.- References.- Problem Index.- Index