Flag-transitive Steiner Designs (Frontiers in Mathematics) - Softcover

Buch 13 von 48: Frontiers in Mathematics

Huber, Michael

 
9783034600019: Flag-transitive Steiner Designs (Frontiers in Mathematics)
Softcover
ISBN 10: 3034600011 ISBN 13: 9783034600019
Verlag: Birkhäuser, 2009

Inhaltsangabe

This monograph provides a full discussion of flag-transitive Steiner designs, a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Críticas

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)

Reseña del editor

This monograph provides a full discussion of flag-transitive Steiner designs, a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
3034600011
ISBN 13 
9783034600019
Einband
Tapa blanda
Anzahl der Seiten
136
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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