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 designsis given in a survey chapter. Fertile interplay of methods from finite group theory, incidence geometry, combinatorics, and number theory Contains a broad introduction with many illustrative examples; accessible to graduate students The author has been awarded a Heinz Maier-Leibnitz-Prize 2008 of the German Research Foundation (DFG) for his work on flag-transitive Steiner designs INDICE: Preface.- 1. Incidence Structures and Steiner Designs.- 2. Permutation Groups and Group Actions.- 3. Number Theoretical Tools.- 4. Highly Symmetric Steiner Designs.- 5. A Census of Highly Symmetric Steiner Designs.- 6. TheClassification of Flag-transitive Steiner Quadruple Systems.- 7. The Classification of Flag-transitive Steiner 3-Designs.- 8. The Classification of Flag-transitive Steiner 4-Designs.- 9. The Classification of Flag-transitive Steiner 5-Designs.- 10. The Non-Existence of Flag-transitive Steiner 6-Designs.- References.- Index.
- ISBN: 978-3-0346-0001-9
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 130
- Fecha Publicación: 01/03/2009
- Nº Volúmenes: 1
- Idioma: Inglés