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Applied Finite Group Actions

  • Book
  • © 1999

Overview

Authors:
  1. Adalbert Kerber

    1. Department of Mathematics, University of Bayreuth, Bayreuth, Germany

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  • This book, written by one of the top-experts in the fields of combinatorics and representation theory, distinguishes itself by its applications-oriented point of view from the existing literature in this field of mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Algorithms and Combinatorics (AC, volume 19)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Labeled Structures

    • Adalbert Kerber
    Pages 1-20

  3. Unlabeled Structures

    • Adalbert Kerber
    Pages 21-52

  4. Enumeration of Unlabeled Structures

    • Adalbert Kerber
    Pages 53-84

  5. Enumeration by Weight

    • Adalbert Kerber
    Pages 85-120

  6. Enumeration by Stabilizer Class

    • Adalbert Kerber
    Pages 121-140

  7. Poset and Semigroup Actions

    • Adalbert Kerber
    Pages 141-168

  8. Representations

    • Adalbert Kerber
    Pages 169-212

  9. Further Applications

    • Adalbert Kerber
    Pages 213-274

  10. Permutations

    • Adalbert Kerber
    Pages 275-316

  11. Construction and Generation

    • Adalbert Kerber
    Pages 317-352

  12. Tables

    • Adalbert Kerber
    Pages 353-396

  13. Appendix

    • Adalbert Kerber
    Pages 397-428

  14. Comments and References

    • Adalbert Kerber
    Pages 429-436

  15. Back Matter

    Pages 437-454
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About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Bayreuth, Bayreuth, Germany

    Adalbert Kerber

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