Flag-transitive Steiner Designs by Michael Huber
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.-
Choquet Integral and Monotone Sublinear Operators
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Exploring Information Geometry
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Lie Models for Spaces
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Hoop Algebras
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Mild Differentiability Conditions for Newton's Method in Banach Spaces
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Heat Kernel on Lie Groups and Maximally Symmetric Spaces
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Direct and Inverse Sturm-Liouville Problems
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Algebraic Approximation: A Guide to Past and Current Solutions
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Advances in the Theory of Varieties of Semigroups
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Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields
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Poncelet Porisms and Beyond
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Stability of Vector Differential Delay Equations
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Applications of Holomorphic Functions in Geometry
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A Primer for a Secret Shortcut to PDEs of Mathematical Physics
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Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube
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Functional Analysis in Asymmetric Normed Spaces
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Topics in Uniform Approximation of Continuous Functions
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Infinite Matrices and their Finite Sections
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Oblique Derivative Problems for Elliptic Equations in Conical Domains
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Approximation of Additive Convolution-Like Operators
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Functions of Omega-Bounded Type
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q-Clan Geometries in Characteristic 2
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Lifting Modules
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Applied Pseudoanalytic Function Theory
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Homotopy Theory of C*-Algebras
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The Geometry of Filtering
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Functional Identities
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Bicomplex Holomorphic Functions
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Module Theory, Extending Modules and Generalizations
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Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws
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Positive Solutions to Indefinite Problems
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Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets
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Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
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Special Functions and Generalized Sturm-Liouville Problems
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Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
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Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
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Shafarevich-Tate Groups
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Variational and Monotonicity Methods in Nonsmooth Analysis
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Quaternionic Approximation
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Newton's Method: an Updated Approach of Kantorovich's Theory
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Introduction to Complex Theory of Differential Equations
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Extremum Problems for Eigenvalues of Elliptic Operators
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Artinian Modules over Group Rings
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Exponentially Convergent Algorithms for Abstract Differential Equations
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Geometric Qp Functions
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Schwarz-Pick Type Inequalities
This monograph provides an excellent development of the existence and nonexistence of flag-transitive and other symmetric Steiner t-designsIn 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)
Huber, Michael: - Michael E. Huber a Chair of GESAMP (Joint Group of Experts on the Scientific Aspects of Marine Environmental Protection).
| SKU | Unavailable |
| ISBN 13 | 9783034600019 |
| ISBN 10 | 3034600011 |
| Title | Flag-transitive Steiner Designs |
| Author | Michael Huber |
| Series | Frontiers In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Birkhauser Verlag AG |
| Year published | 2009-02-19 |
| Number of pages | 125 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |