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.
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
5
5 s/w Abbildungen
XIV, 362 p. 5 illus.
Dateigröße
ISBN-13
978-1-4757-2497-4 (9781475724974)
DOI
10.1007/978-1-4757-2497-4
Schweitzer Klassifikation
1 A Bridge Club Design.- 2 The First Time.- 3 Computational Methods in Design Theory.- 4 Finding Designs with Genetic Algorithms.- 5 Making the Mols Table.- 6 On Writing Isomorphism Programs.- 7 The Nonexistence of 4-(12,6,6) Designs.- 8 Bibds with k = 6 and ? = 1.- 9 Polyhedral Methods in Design Theory.- 10 Another Look at Large Sets of Steiner Triple Systems.- 11 (22, 33,12, 8, 4)-BIBD, AN UPDATE.
