Convexity In Discrete Structures
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Convexity In Discrete Structures
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Author : Manoj Changat
language : en
Publisher:
Release Date : 2010
Convexity In Discrete Structures written by Manoj Changat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Convex domains categories.
Discrete Convex Analysis
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Author : Kazuo Murota
language : en
Publisher: SIAM
Release Date : 2003-01-01
Discrete Convex Analysis written by Kazuo Murota and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis. Discrete Convex Analysis provides the information that professionals in optimization will need to "catch up" with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks.
Theory Of Convex Structures
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Author : M.L.J. van de Vel
language : en
Publisher: Elsevier
Release Date : 1993-08-02
Theory Of Convex Structures written by M.L.J. van de Vel and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-02 with Mathematics categories.
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.
Convexity And Graph Theory
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Author : M. Rosenfeld
language : en
Publisher: Elsevier
Release Date : 1984-01-01
Convexity And Graph Theory written by M. Rosenfeld and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
Convexity In Discrete Structures
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Author : Manoj Changat
language : en
Publisher:
Release Date : 2008
Convexity In Discrete Structures written by Manoj Changat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Convex domains categories.
Convexity And Discrete Geometry Including Graph Theory
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Author : Karim Adiprasito
language : en
Publisher: Springer
Release Date : 2016-05-02
Convexity And Discrete Geometry Including Graph Theory written by Karim Adiprasito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-02 with Mathematics categories.
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
Convex And Discrete Geometry
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Author : Peter M. Gruber
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-17
Convex And Discrete Geometry written by Peter M. Gruber 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 2007-05-17 with Mathematics categories.
Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers, and useful to people working in the applied fields.
Geodesic Convexity In Graphs
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Author : Ignacio M. Pelayo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-06
Geodesic Convexity In Graphs written by Ignacio M. Pelayo 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 2013-09-06 with Mathematics categories.
Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.
Convexity And Concentration
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Author : Eric Carlen
language : en
Publisher: Springer
Release Date : 2017-04-20
Convexity And Concentration written by Eric Carlen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-20 with Mathematics categories.
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.
Combinatorial Convexity
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Author : Imre Bárány
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-04
Combinatorial Convexity written by Imre Bárány 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 2021-11-04 with Education categories.
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.