Huber M. Flag-transitive Steiner Designs

Basel: Birkhäuser, 2009. — 136 p.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.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