Classification Algorithms for Codes and Designs: 15 - Brossura
Libro 5 di 24: Algorithms and Computation in Mathematics
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
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)
Contenuti
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
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A new starting-point and a new method are requisite, to insure a complete [classi cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work - on various objects, including (what became later known as) Steiner triple systems - led to several classi cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e ective (often to prove nonexistence or uniqueness), classi cation in general is about algorithms and computation. 428 pp. Englisch. Codice articolo 9783642432507
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Excellent interdisciplinary monograph on highly applications relevant topicProvides the first comprehensive reference on combinatorial classification algorithmsAddresses both the general theory and application to central families of c. Codice articolo 11800926
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Taschenbuch. Condizione: Neu. Classification Algorithms for Codes and Designs | Petteri Kaski (u. a.) | Taschenbuch | Algorithms and Computation in Mathematics | xi | Englisch | 2014 | Springer | EAN 9783642432507 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Codice articolo 104913868
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 428 pp. Englisch. Codice articolo 9783642432507
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - A new starting-point and a new method are requisite, to insure a complete [classi cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work - on various objects, including (what became later known as) Steiner triple systems - led to several classi cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e ective (often to prove nonexistence or uniqueness), classi cation in general is about algorithms and computation. Codice articolo 9783642432507
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