
Applied Finite Group Actions
Adalbert Kerber(Author)
Springer (Publisher)
2nd Edition
Published on 15. December 2010
Book
Paperback/Softback
XXV, 454 pages
978-3-642-08522-2 (ISBN)
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.
More details
Series
Edition
Second Edition 1999
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XXV, 454 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 27 mm
Weight
727 gr
ISBN-13
978-3-642-08522-2 (9783642085222)
DOI
10.1007/978-3-662-11167-3
Schweitzer Classification
Other editions
Additional editions

Adalbert Kerber
Applied Finite Group Actions
Book
08/1999
2nd Edition
Springer
€160.49
Shipment within 7-9 days
Content
0. Labeled Structures.- 1. Unlabeled Structures.- 2. Enumeration of Unlabeled Structures.- 3. Enumeration by Weight.- 4. Enumeration by Stabilizer Class.- 5. Poset and Semigroup Actions.- 6. Representations.- 7. Further Applications.- 8. Permutations.- 9. Construction and Generation.- 10. Tables.- 11. Appendix.- 12. Comments and References.- References.