Diagram Groups
Diagram Groups

Author: Victor Guba

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 130

ISBN-13: 0821806394

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Diagram groups are groups consisting of spherical diagrams (pictures) over monoid presentations. They can be also defined as fundamental groups of the Squier complexes associated with monoid presentations. The authors show that the class of diagram groups contains some well-known groups, such as the R. Thompson group F. This class is closed under free products, finite direct products, and some other group-theoretical operations. The authors develop combinatorics on diagrams similar to the combinatorics on words. This helps in finding some structure and algorithmic properties of diagram groups. Some of these properties are new even for R. Thompson's group F. In particular, the authors describe the centralizers of elements in F, prove that it has solvable conjugacy problems, etc.

Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications
Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications

Author: Surender Kumar Jain

Publisher: American Mathematical Soc.

Published: 2008

Total Pages: 242

ISBN-13: 0821842854

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Articles in this volume are based on talks given at the International Conference on Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications. The conference provided researchers in mathematics with the opportunity to discuss new developments in these rapidly growing fields. This book contains several excellent articles, both expository and original, with new and significant results. It is suitable for graduate students and researchers interested in Ring Theory,Diagram Algebras and related topics.

Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook
Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook

Author: Svetlana N. Yanushkevich

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 952

ISBN-13: 1420037587

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Decision diagram (DD) techniques are very popular in the electronic design automation (EDA) of integrated circuits, and for good reason. They can accurately simulate logic design, can show where to make reductions in complexity, and can be easily modified to model different scenarios. Presenting DD techniques from an applied perspective, Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook provides a comprehensive, up-to-date collection of DD techniques. Experts with more than forty years of combined experience in both industrial and academic settings demonstrate how to apply the techniques to full advantage with more than 400 examples and illustrations. Beginning with the fundamental theory, data structures, and logic underlying DD techniques, they explore a breadth of topics from arithmetic and word-level representations to spectral techniques and event-driven analysis. The book also includes abundant references to more detailed information and additional applications. Decision Diagram Techniques for Micro- and Nanoelectronic Design Handbook collects the theory, methods, and practical knowledge necessary to design more advanced circuits and places it at your fingertips in a single, concise reference.

Diagram Geometry
Diagram Geometry

Author: Francis Buekenhout

Publisher: Springer Science & Business Media

Published: 2013-01-26

Total Pages: 597

ISBN-13: 3642344534

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This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.

Diagram Cohomology and Isovariant Homotopy Theory
Diagram Cohomology and Isovariant Homotopy Theory

Author: Giora Dula

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 97

ISBN-13: 0821825895

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Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.

Diagram Techniques in Group Theory
Diagram Techniques in Group Theory

Author: Geoffrey E. Stedman

Publisher: Cambridge University Press

Published: 2009-09-17

Total Pages: 0

ISBN-13: 9780521119702

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This book, first published in 1990, gives a general account of diagram manipulation techniques, as alternatives to algebraic methods of proof, in theoretical physics. Methods reviewed by the author include the popular techniques pioneered by Jucys and collaborators in the quantum theory of angular momentum and by Feynman in quantum field theory. The reader is encouraged to become bilingual in that many steps in the argument are presented as Problems, and are immediately followed by solutions and by comments on the method or proof and the significance of the results. This book will be of value to graduate students and research workers in theoretical solid state physics, atomic, molecular, nuclear and particle physics and theoretical chemistry.