Combinatorial Structures In Algebra And Geometry
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Combinatorics And Finite Geometry
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Author : Steven T. Dougherty
language : en
Publisher: Springer Nature
Release Date : 2020-10-30
Combinatorics And Finite Geometry written by Steven T. Dougherty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Mathematics categories.
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.
Combinatorial Structures In Algebra And Geometry
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Author : Dumitru I. Stamate
language : en
Publisher: Springer Nature
Release Date : 2020-09-01
Combinatorial Structures In Algebra And Geometry written by Dumitru I. Stamate and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.
This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1).
Combinatorial Algebraic Topology
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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24
Combinatorial Algebraic Topology written by Dimitry Kozlov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-24 with Mathematics categories.
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Algorithms In Combinatorial Geometry
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Author : Herbert Edelsbrunner
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-07-31
Algorithms In Combinatorial Geometry written by Herbert Edelsbrunner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-07-31 with Computers categories.
Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
Combinatorial Mathematics
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Author : Douglas B. West
language : en
Publisher: Cambridge University Press
Release Date : 2021
Combinatorial Mathematics written by Douglas B. West and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.
Lectures In Geometric Combinatorics
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Author : Rekha R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Lectures In Geometric Combinatorics written by Rekha R. Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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 state polytope 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 from commutative 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.
Fundamental Structures Of Algebra And Discrete Mathematics
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Author : Stephan Foldes
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-14
Fundamental Structures Of Algebra And Discrete Mathematics written by Stephan Foldes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-14 with Mathematics categories.
Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Combinatorial And Computational Geometry
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Author : Jacob E. Goodman
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-08
Combinatorial And Computational Geometry written by Jacob E. Goodman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Computers categories.
This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Combinatorics Of Coxeter Groups
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Author : Anders Bjorner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-25
Combinatorics Of Coxeter Groups written by Anders Bjorner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-25 with Mathematics categories.
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
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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Author : Takayuki Hibi
language : en
Publisher: World Scientific
Release Date : 2019-05-30
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes written by Takayuki Hibi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-30 with Mathematics categories.
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.