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  • Book
  • © 1999

Applied Finite Group Actions

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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
  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

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

Bibliographic Information

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access