Classification Algorithms for Codes and Designs (Algorithms

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

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 â€“ on various objects, including (what became later known as) Steiner triple systems â€“ 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.

Country	USA
Binding	Hardcover
Brand	Brand: Springer
EAN	9783540289906
Edition	2006
Feature	Used Book in Good Condition
ISBN	3540289909
Label	Springer
Manufacturer	Springer
MPN	62 black & white illustrations, 30 black
NumberOfItems	1
NumberOfPages	412
PartNumber	62 black & white illustrations, 30 black
PublicationDate	2005-12-22
Publisher	Springer
Studio	Springer
ReleaseDate	0000-00-00

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