Overview

"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."

Full Product Details

Author:   Adalbert Kerber
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 2nd ed. 1999
Volume:   19
Dimensions:   Width: 15.50cm , Height: 2.40cm , Length: 23.50cm
Weight:   0.736kg
ISBN:  

9783642085222

ISBN 10:   3642085229
Pages:   454
Publication Date:   15 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

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.

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