Author: Gregory L. Cherlin
Publisher: Princeton University Press
ISBN: 9780691113319
Category : Mathematics
Languages : en
Pages : 204
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Book Description
This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated analysis of computational issues, and an "intrinsic" characterization of the permutation groups (or finite structures) under consideration. The main finiteness theorem shows that the structures under consideration fall naturally into finitely many families, with each family parametrized by finitely many numerical invariants (dimensions of associated coordinating geometries). The authors provide a case study in the extension of methods of stable model theory to a nonstable context, related to work on Shelah's "simple theories." They also generalize Lachlan's results on stable homogeneous structures for finite relational languages, solving problems of effectivity left open by that case. Their methods involve the analysis of groups interpretable in these structures, an analog of Zilber's envelopes, and the combinatorics of the underlying geometries. Taking geometric stability theory into new territory, this book is for mathematicians interested in model theory and group theory.
Author: Luigi A. Rosati
Publisher: Springer
ISBN: 3540398015
Category : Mathematics
Languages : en
Pages : 287
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Book Description
Author: M. Aigner
Publisher: Springer
ISBN: 3540386394
Category : Mathematics
Languages : en
Pages : 262
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Book Description
Dedicated to Professor Dr. Hanfried Lenz on the Occasion of his 65th Birthday
Author: L. Salvadori
Publisher: Springer
ISBN: 3540388125
Category : Mathematics
Languages : en
Pages : 242
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Book Description
Author: R.L. Graham
Publisher: Elsevier
ISBN: 008093384X
Category : Computers
Languages : en
Pages : 2404
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Book Description
Handbook of Combinatorics
Author: Katrin Tent
Publisher: Cambridge University Press
ISBN: 9780521010634
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.
Author: N.S. Narasimha Sastry
Publisher: Springer
ISBN: 9811320470
Category : Mathematics
Languages : en
Pages : 213
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Book Description
This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.
Author: Bozzano G Luisa
Publisher: Elsevier
ISBN: 0080933351
Category : Computers
Languages : en
Pages : 1121
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Book Description
Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.
Author: S. Greco
Publisher: Springer
ISBN: 3540390898
Category : Mathematics
Languages : en
Pages : 309
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Book Description
Author: Amritanshu Prasad
Publisher: Cambridge University Press
ISBN: 1107082056
Category : Mathematics
Languages : en
Pages : 205
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Book Description
This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
