Computational And Constructive Design Theory
Download Computational And Constructive Design Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Computational And Constructive Design Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Computational and Constructive Design Theory
Author: W.D. Wallis
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs.
Designs 2002
This volume is a sequel to our 1996 compilation, Computational and Constructive Design Theory. Again we concentrate on two closely re lated aspects of the study of combinatorial designs: design construction and computer-aided study of designs. There are at least three classes of constructive problems in design theory. The first type of problem is the construction of a specific design. This might arise because that one particular case is an exception to a general rule, the last remaining case of a problem, or the smallest unknown case. A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of "starter" designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding "starter" designs.
Surveys in Combinatorics 2003
Author: C. D. Wensley
language: en
Publisher: Cambridge University Press
Release Date: 2003-07-24
The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.