Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics) by Petteri Kaski, PDF 3642432506

Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)

  • Title: Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
  • Autor: Petteri Kaski
  • Publisher (Publication Date): Springer; 2006 edition (November 20, 2014)
  • Language: English
  • ISBN-10: | 3642432506
  • ISBN-13: | 978-3642432507
  • File Format: EPUB, PDF

 
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.

No reviews

Comments:


Related posts

Online Teaching at Its Best: Merging Instructional Design with Teaching and Learning Research by Ludwika A. Goodson , PDF
Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic Systems by Adrian-Mihail Stoica, PDF 1441906312
Financial Accounting with Odoo, Second Edition: Versions 6-10 by Maxime Chambreuil, PDF 1533001952
Software Quality Assurance: Principles and Practices by Nina S. Godbole, PDF 184265702X
Microsoft Dynamics AX Implementation Guide by Yogesh Kasat, PDF 1785288962
The Socio-economic Impacts of Telecentres in Rural Tanzania: A Case Study of Sengerema District Council, Mwanza Region by Boniface Mbangala, PDF 3659783773

Leave a Reply

Your email address will not be published. Required fields are marked *