Geometric Combinatorics
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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 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.
Geometric Combinatorics
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Author : Ezra Miller
language : en
Publisher: American Mathematical Soc.
Release Date :
Geometric Combinatorics written by Ezra Miller 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 with Mathematics categories.
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
Algebraic And Geometric Combinatorics
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Author : Christos A. Athanasiadis
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Algebraic And Geometric Combinatorics written by Christos A. Athanasiadis 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 volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.
Algebraic And Geometric Combinatorics
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Author : E. Mendelsohn
language : en
Publisher: Elsevier
Release Date : 1982-01-01
Algebraic And Geometric Combinatorics written by E. Mendelsohn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
Algebraic and Geometric Combinatorics
Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics
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Author : Matthias Beck
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-12
Combinatorial Reciprocity Theorems An Invitation To Enumerative Geometric Combinatorics written by Matthias Beck 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 2018-12-12 with Combinatorial analysis categories.
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
Algebraic And Geometric Combinatorics On Lattice Polytopes Proceedings Of The Summer Workshop On Lattice Polytopes
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Author : Hibi Takayuki
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 Hibi Takayuki 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.
Geometric Combinatorics
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Author : Ezra Miller
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Geometric Combinatorics written by Ezra Miller 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 2007 with Combinatorial analysis categories.
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.
Geometric Discrepancy
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Author : Jiri Matousek
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02
Geometric Discrepancy written by Jiri Matousek 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 2009-12-02 with Mathematics categories.
What is the "most uniform" way of distributing n points in the unit square? How big is the "irregularity" necessarily present in any such distribution? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.
Geometry And Combinatorics
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Author : J. J. Seidel
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Geometry And Combinatorics written by J. J. Seidel and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Geometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.
Geometric Etudes In Combinatorial Mathematics
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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-15
Geometric Etudes In Combinatorial Mathematics written by Alexander Soifer 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 2010-06-15 with Mathematics categories.
Geometric Etudes in Combinatorial Mathematics is not only educational, it is inspirational. This distinguished mathematician captivates the young readers, propelling them to search for solutions of life’s problems—problems that previously seemed hopeless. Review from the first edition: The etudes presented here are not simply those of Czerny, but are better compared to the etudes of Chopin, not only technically demanding and addressed to a variety of specific skills, but at the same time possessing an exceptional beauty that characterizes the best of art...Keep this book at hand as you plan your next problem solving seminar. —The American Mathematical Monthly