| Description |
1 online resource (xii, 412 pages) : 62 figure, 30 table |
| Series |
Algorithms and computation in mathematics, 1431-1550 ; v. 15 |
|
Algorithms and computation in mathematics ; v. 15. 1431-1550
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| Contents |
Cover -- Table of Contents -- 1 Introduction -- 2 Graphs, Designs, and Codes -- 2.1 Graphs -- 2.2 Designs -- 2.3 Codes -- 2.4 More Combinatorial Objects -- 3 Representations and Isomorphism -- 3.1 Finite Groups and Group Actions -- 3.2 Categories and Equivalence -- 3.3 Isomorphism Computations -- 4 Isomorph-Free Exhaustive Generation -- 4.1 Exhaustive Generation -- 4.2 Techniques for Isomorph Rejection -- 5 Auxiliary Algorithms -- 5.1 Clique Algorithms -- 5.2 Exact Cover Algorithms -- 5.3 Set Cover Algorithms -- 5.4 Diophantine Linear Systems of Equations -- 5.5 Permutation Group Algorithms -- 5.6 Isomorphism Algorithms -- 5.7 Distributing Computer Search -- 6 Classification of Designs -- 6.1 Balanced Incomplete Block Designs -- 6.2 t-Designs -- 6.3 Resolutions of Designs -- 6.4 Designs with Additional Properties -- 7 Classification of Codes -- 7.1 Error-Correcting Codes -- 7.2 Covering Codes -- 7.3 Linear Codes -- 8 Classification of Related Structures -- 8.1 Triple Systems -- 8.2 Hadamard Matrices -- 8.3 Orthogonal Arrays -- 9 Prescribing Automorphism Groups -- 9.1 Preliminaries -- 9.2 Designs -- 9.3 Codes -- 9.4 Other Objects -- 10 Validity of Computational Results -- 10.1 Errors and Remedies -- 10.2 Double Counting Using the Orbit-Stabilizer Theorem -- 10.3 Double Counting by Identifying Subobjects -- 10.4 Some Final Observations -- 11 Computational Complexity -- 11.1 Preliminaries -- 11.2 Completion Problems -- 11.3 Isomorphism Problems -- 11.4 Classification Problems -- 12 Nonexistence of Projective Planes of Order 10 -- 12.1 Projective Planes of Order 10 -- 12.2 Codes of Designs -- 12.3 The Main Search -- References -- Problem Index |
| Summary |
"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."--Jacket |
| Bibliography |
Includes bibliographical references (pages 365-398) and index.) |
| Notes |
English |
|
Print version record |
| Subject |
Combinatorial group theory.
|
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MATHEMATICS -- Group Theory.
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Grupos, Teoría combinatoria de
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Combinatorial group theory
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Configurações combinatórias.
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Teoria dos códigos.
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| Form |
Electronic book
|
| Author |
Östergård, Patric R. J
|
| ISBN |
9783540289913 |
|
3540289917 |
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3540289909 |
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9783540289906 |
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3642432506 |
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9783642432507 |
|
