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An Algebraic Approach to Association Schemes
  • Language: en
  • Pages: 201

An Algebraic Approach to Association Schemes

  • Type: Book
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  • Published: 2006-11-13
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  • Publisher: Springer

The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups. The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when the theory of generators is developed. Here, the buildings play the role which, in group theory, is played by the Coxeter groups. - The text is intended for students as well as for researchers in algebra, in particular in algebraic combinatorics.

Hypergroups
  • Language: en
  • Pages: 398

Hypergroups

This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and/or Algebraic Combinatorics, in particular on association schemes.

Theory of Association Schemes
  • Language: en
  • Pages: 295

Theory of Association Schemes

This book is a concept-oriented treatment of the structure theory of association schemes. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type.

Combinatorics '86
  • Language: en
  • Pages: 519

Combinatorics '86

  • Type: Book
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  • Published: 2011-09-22
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  • Publisher: Elsevier

Recent developments in all aspects of combinatorial and incidence geometry are covered in this volume, including their links with the foundations of geometry, graph theory and algebraic structures, and the applications to coding theory and computer science.Topics covered include Galois geometries, blocking sets, affine and projective planes, incidence structures and their automorphism groups. Matroids, graph theory and designs are also treated, along with weak algebraic structures such as near-rings, near-fields, quasi-groups, loops, hypergroups etc., and permutation sets and groups.The vitality of combinatorics today lies in its important interactions with computer science. The problems which arise are of a varied nature and suitable techniques to deal with them have to be devised for each situation; one of the special features of combinatorics is the often sporadic nature of solutions, stemming from its links with number theory. The branches of combinatorics are many and various, and all of them are represented in the 56 papers in this volume.

Evolutionary Dynamics
  • Language: en
  • Pages: 492

Evolutionary Dynamics

The 14 chapters of this volume, which present an overview of new research in evolutionary dynamics, were first presented at a conference held in October 1998 at the Santa Fe Institute. The main divisions of the book are macroevolution; epochal evolution; population genetics, dynamics, and optimization; and evolution of cooperation. Individual topics include spectral landscape theory, external triggers in biological evolution, and evolutionary dynamics of asexual reproduction. Several of the contributors, like the editors, are affiliated with the Sante Fe Institute; others teach or work in physics, genetics, biology, computational neuroscience, and theoretical chemistry at universities and private institutions in the US, UK, Austria, Sweden, Australia, Israel, and Germany. Annotation copyrighted by Book News, Inc., Portland, OR

Songs for Cabo Verde
  • Language: en
  • Pages: 342

Songs for Cabo Verde

Chronicles the work of Norberto Tavares, a Cabo Verdean musician and humanitarian who served as the conscience of his island nation during the transition from Portuguese colony to democratic republic.

Erdos-Ko-Rado Theorems: Algebraic Approaches
  • Language: en
  • Pages: 353

Erdos-Ko-Rado Theorems: Algebraic Approaches

Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.

Abstracts of Papers Presented to the American Mathematical Society
  • Language: en
  • Pages: 754

Abstracts of Papers Presented to the American Mathematical Society

  • Type: Book
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  • Published: 2007
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  • Publisher: Unknown

None

Theory of Association Schemes
  • Language: en
  • Pages: 314

Theory of Association Schemes

This book is a concept-oriented treatment of the structure theory of association schemes. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type.

Groups and Graphs, Designs and Dynamics
  • Language: en
  • Pages: 452

Groups and Graphs, Designs and Dynamics

This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.