APPLIED FINITE GROUP ACTIONS

Kerber, Adalbert

ISBN 10: 3540659412 / ISBN 13: 9783540659419

Published by Springer-Verlag, Berlin, Heidelberg, New York, 1999

Octavo, viii, x, xiii, xxv, 454 pages. In Very Good condition. Bound in the publisher's yellow cloth with black lettering to spine. Boards have slight wear exteriorly. Text block has very light age toning to the edges. Illustrated. Second edition, revised and expanded. NOTE: Shelved in Netdesk Column D, ND-D. 1377399. FP New Rockville Stock. Seller Inventory # 1377399

Synopsis:

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.

From the Back Cover: The topic of this book is finite group actions and their use in order to approach finite unlabeled structures by defining them as orbits of finite groups of sets. Well-known examples are graphs, linear codes, chemical isomers, spin configurations, isomorphism classes of combinatorial designs etc.
This second edition is an extended version and puts more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.
This book will be of great use to researchers and graduate students.

Bibliographic Details

Title: APPLIED FINITE GROUP ACTIONS
Publisher: Springer-Verlag, Berlin, Heidelberg, New York
Publication Date: 1999
Binding: Hardcover
Edition: Second Edition.