Author : Günter Ewald
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 33,89 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461240441
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Author : Rekha R. Thomas
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 34,48 MB
Release : 2006
Category : Mathematics
ISBN : 9780821841402
This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the statepolytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics. The connections rely on Grobner bases of toric ideals and other methods fromcommutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.
Author : János Pach
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 44,67 MB
Release : 2011-10-18
Category : Mathematics
ISBN : 1118031369
A complete, self-contained introduction to a powerful and resurgingmathematical discipline . Combinatorial Geometry presents andexplains with complete proofs some of the most important resultsand methods of this relatively young mathematical discipline,started by Minkowski, Fejes Toth, Rogers, and Erd???s. Nearly halfthe results presented in this book were discovered over the pasttwenty years, and most have never before appeared in any monograph.Combinatorial Geometry will be of particular interest tomathematicians, computer scientists, physicists, and materialsscientists interested in computational geometry, robotics, sceneanalysis, and computer-aided design. It is also a superb textbook,complete with end-of-chapter problems and hints to their solutionsthat help students clarify their understanding and test theirmastery of the material. Topics covered include: * Geometric number theory * Packing and covering with congruent convex disks * Extremal graph and hypergraph theory * Distribution of distances among finitely many points * Epsilon-nets and Vapnik--Chervonenkis dimension * Geometric graph theory * Geometric discrepancy theory * And much more
Author : Francois Bergeron
Publisher : CRC Press
Page : 227 pages
File Size : 25,72 MB
Release : 2009-07-06
Category : Mathematics
ISBN : 1439865078
Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and
Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 31,87 MB
Release : 2020-10-30
Category : Mathematics
ISBN : 3030563952
This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
Author : Takayuki Hibi
Publisher : World Scientific
Page : 476 pages
File Size : 28,36 MB
Release : 2019-05-30
Category : Mathematics
ISBN : 9811200491
This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.
Author : Linfan Mao
Publisher : Infinite Study
Page : 502 pages
File Size : 31,80 MB
Release : 2011
Category : Combinatorial geometry
ISBN : 159973155X
Author : Anders Bjorner
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 18,41 MB
Release : 2006-02-25
Category : Mathematics
ISBN : 3540275967
Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
Author : Martin W. Liebeck
Publisher : Cambridge University Press
Page : 505 pages
File Size : 49,58 MB
Release : 1992-09-10
Category : Mathematics
ISBN : 0521406854
This volume contains a collection of papers on the subject of the classification of finite simple groups.
Author : Linfan Mao
Publisher : Infinite Study
Page : 499 pages
File Size : 36,12 MB
Release : 2009
Category : Mathematics
ISBN : 1599731002
This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.
