Flag-transitive Steiner Designs

Overview

The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, like finite or incidence geometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently self-contained and unified manner the classification of all flag-transitive Steiner designs is presented. This recent result settles interesting and challenging questions that ...

See more details below
Paperback (2009)
$36.16
BN.com price
(Save 9%)$39.95 List Price
Other sellers (Paperback)
  • All (5) from $30.45   
  • New (4) from $30.45   
  • Used (1) from $72.99   
Sending request ...

Overview

The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, like finite or incidence geometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently self-contained and unified manner the classification of all flag-transitive Steiner designs is presented. This recent result settles interesting and challenging questions that have been object of research for more than 40 years. Its proof combines methods from finite group theory, incidence geometry, combinatorics, and number theory.

The book contains a broad introduction to the topic, along with many illustrative examples. Moreover, a census of some of the most general results on highly symmetric Steiner designs is given in a survey chapter.

The monograph is addressed to graduate students in mathematics and computer science as well as established researchers in design theory, finite or incidence geometry, coding theory, cryptography, algebraic combinatorics, and more generally, discrete mathematics.

Read More Show Less

Editorial Reviews

From the Publisher
This monograph provides an excellent development of the existence and nonexistence of flag-transitive and other symmetric Steiner t-designs. In particular, it develops a complete classification of all flag-transitive Steiner t-designs for strength t at least three.
The topic is a beautiful mixture of algebra and combinatorics, and it impinges on many applications areas. Of particular value is the material providing the necessary background in group theory, incidence geometry, number theory, and combinatorial design theory to support a complete exposition of the many results. These form the focus of the first three chapters. Chapter 4 then develops results on symmetric actions of groups on Steiner systems, and provides many helpful examples. Chapter 5 then states the main existence result for flag-transitive Steiner systems, and places this in the context of related existence results for highly symmetric actions. Chapters 6 through
10 fill in the details of the existence proof. Steiner quadruple systems are treated in
Chapter 6, while strength three in general is treated in Chapter 7. Chapters 8 and 9
then treat the cases of strengths four and five, respectively. Finally Chapter 10 provides the proof that no flag-transitive Steiner 6-design exists.
The presentation is lucid and accessible. Indeed the author has done a first rate job of presenting material that involves many deep ideas and a number of technical issues. At the same time, the monograph indicates useful next steps to take in the research topic.

Zentralblatt Math - Charles J. Colbourn (Tempe)

Read More Show Less

Product Details

  • ISBN-13: 9783034600019
  • Publisher: Birkhauser Basel
  • Publication date: 5/11/2009
  • Series: Frontiers in Mathematics Series
  • Edition description: 2009
  • Edition number: 1
  • Pages: 125
  • Product dimensions: 6.60 (w) x 9.30 (h) x 0.30 (d)

Table of Contents

Incidence Structures and Steiner Designs.- Permutation Groups and Group Actions.- Number Theoretical Tools.- Highly Symmetric Steiner Designs.- A Census of Highly Symmetric Steiner Designs.- The Classification of Flag-transitive Steiner Quadruple Systems.- The Classification of Flag-transitive Steiner 3-Designs.- The Classification of Flag-transitive Steiner 4-Designs.- The Classification of Flag-transitive Steiner 5-Designs.- The Non-Existence of Flag-transitive Steiner 6-Designs.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)