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Permutation groups are one of the oldest topics in algebra. However, their study has recently been revolutionised by new developments, particularly the classification of finite simple groups, but also relations with logic and combinatorics, and importantly, computer algebra systems have been introduced that can deal with large permutation groups. This book gives a summary of these developments, including an introduction to relevant computer algebra systems, sketch proofs of major theorems, and many examples of applying the classification of finite simple groups. It is aimed at beginning graduate students and experts in other areas, and grew from a short course at the EIDMA institute in Eindhoven.

Permutation groups --- Permutation groups. --- Groupes de permutations --- Substitution groups --- Group theory

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These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other topics from the whole range of combinatorial theory and permutation groups. These include network flows, perfect codes, Latin squares, block designs and multiply-transitive permutation groups, and long and detailed appendices are provided to serve as introductions to these various subjects. Many of the results are published for the first time.

Combinatorial designs and configurations. --- Permutation groups. --- Parallels (Geometry) --- Configurations and designs, Combinatorial --- Designs and configurations, Combinatorial --- Combinatorial analysis --- Geometry --- Geometry, Non-Euclidean --- Substitution groups --- Group theory --- Foundations

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Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra. Many exercises and useful hints are included througout, and a large number of references are given.

Combinatorial designs and configurations. --- Coding theory. --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Configurations and designs, Combinatorial --- Designs and configurations, Combinatorial --- Extremal problems

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These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs on the one hand, and graph theory on the other. A feature of this book is the discussion of then-recent construction of t-designs from codes. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.

Block designs. --- Coding theory. --- Graph theory. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Designs, Block --- Combinatorial designs and configurations --- Experimental design --- Extremal problems --- Block designs --- CODING THEORY

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Originally published in 1981, this collection of 33 research papers follows from a conference on the interwoven themes of finite Desarguesian spaces, Steiner systems, coding theory, group theory, block designs, generalized quadrangles, and projective planes. There is a comprehensive introduction, which aims to interest the non-specialist in the subject and which indicates how the contributions fit together. This is a field of research pursued both for its intrinsic interest and its applications. These papers include a number of open problems whose statement requires very little mathematical sophistication.

Finite geometries. --- Combinatorial designs and configurations. --- Configurations and designs, Combinatorial --- Designs and configurations, Combinatorial --- Combinatorial analysis --- Geometries, Finite --- Combinatorial geometry