| Applied Finite Group Actions Contributor(s): Kerber, Adalbert (Author) |
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ISBN: 3642085229 ISBN-13: 9783642085222 Publisher: Springer OUR PRICE: $161.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Medical - Mathematics | Discrete Mathematics |
| Dewey: 512.2 |
| Series: Algorithms and Combinatorics |
| Physical Information: 0.97" H x 6.14" W x 9.21" (1.48 lbs) 454 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Also the present second edition of this book is an introduction to the theory of clas- sification, enumeration, construction and generation of finite unlabeled structures in mathematics and sciences. Since the publication of the first edition in 1991 the constructive theory of un- labeled finite structures has made remarkable progress. For example, the first- designs with moderate parameters were constructed, in Bayreuth, by the end of 1994 ([9]). The crucial steps were - the prescription of a suitable group of automorphisms, i. e. a stabilizer, and the corresponding use of Kramer-Mesner matrices, together with - an implementation of an improved version of the LLL-algorithm that allowed to find 0-1-solutions of a system of linear equations with the Kramer-Mesner matrix as its matrix of coefficients. of matrices of the The Kramer-Mesner matrices can be considered as submatrices form A" (see the chapter on group actions on posets, semigroups and lattices). They are associated with the action of the prescribed group G which is a permutation group on a set X of points induced on the power set of X. Hence the discovery of the first 7-designs with small parameters is due to an application of finite group actions. This method used by A. Betten, R. Laue, A. Wassermann and the present author is described in a section that was added to the manuscript of the first edi- tion. |