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Author: Richard K. Guy
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 536
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Book Description
Author: Richard K. Guy
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 536
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Book Description
Author: François Bergeron
Publisher: Cambridge University Press
ISBN: 9780521573238
Category : Mathematics
Languages : en
Pages : 484
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Book Description
The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.
Author: Donald L. Kreher
Publisher: CRC Press
ISBN: 9780849339882
Category : Mathematics
Languages : en
Pages : 346
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Book Description
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as: Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
Author: Dumitru I. Stamate
Publisher: Springer Nature
ISBN: 3030521117
Category : Mathematics
Languages : en
Pages : 185
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Book Description
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).
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: Jesús Mario Bilbao
Publisher: Springer Science & Business Media
ISBN: 1461543932
Category : Business & Economics
Languages : en
Pages : 329
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Book Description
The aim of Cooperative Games on Combinatorial Structures is to analyze conflict situations in which two or more players can make coalitions and obtain prizes and penalties. This approach to situations of competition and cooperation was given in the seminal treatise by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior. Cooperative game theory has succeeded in providing many applications of game theory. In this volume, games defined on combinatorial structures will be analyzed, i.e. a set system over a set of players. In many situations the author will work in a closure space. Examples of closure operators are the spanning operator of linear algebra and all convex hull operators. Chapters 1-4 constitute a review of mathematical concepts from Cooperative Game Theory, Graph Theory, Linear and Integer Programming, Combinatorial Optimization, Discrete Convex Analysis and Computational Complexity. The table of contents is a short guide to the topics and methods covered in this book. In Chapters 11 and 12, several notebooks are presented with the system Mathematica by Wolfram in the contexts of the packages DiscreteMath (Skiena) and Cooperative (Carter). There will also be found in the book several research projects. These are intended to offer new ideas that the reader should consider with caution. This book will be of interest to graduate students with some experience in game theory or mathematical programming and professional researchers in game theory, operational research and its applications in economic theory, and the political and social sciences. In addition, it will be especially useful for professionals who are interested in models for understanding and managing conflicts: management and operational research scientists, political and military scientists, and professional negotiators.
Author: ATKIN
Publisher: Birkhäuser
ISBN: 3034857500
Category : Social Science
Languages : en
Pages : 253
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Book Description
This book is a presentation of my recent research work into the theory and applications of mathematical relations between finite sets. The consequent results and concepts are expressed in 'conjunction' with the idea of a union of simplicial complexes and the algorithms and overall methodology have become known as Q-Analysis. The mathematical ideas are essentially comhinatorial and are developed in Section-A of the book, whilst Section-R contains an application to a community study (that of the IJniversity of Rssex). All of the work has been published elsewhere, in the usual form of papers, and a comprehensive introduction to the whole approach will be found in my earlier book, Mathematical Structure in Human Affairs (Heinemann, London 1974). Much of the research work referred to in this present hook would not have been possible without the co-operation of my research team, of whom I would particularly like to thank J.II. Johnson, and its puhlication owes a lot to the secretarial help provided by ~Iary Low. R.H. Atkin IJniversity of Rssex U.K.
Author: Efi Fogel
Publisher: Springer Science & Business Media
ISBN: 3642172830
Category : Computers
Languages : en
Pages : 307
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Book Description
Arrangements of curves constitute fundamental structures that have been intensively studied in computational geometry. Arrangements have numerous applications in a wide range of areas – examples include geographic information systems, robot motion planning, statistics, computer-assisted surgery and molecular biology. Implementing robust algorithms for arrangements is a notoriously difficult task, and the CGAL arrangements package is the first robust, comprehensive, generic and efficient implementation of data structures and algorithms for arrangements of curves. This book is about how to use CGAL two-dimensional arrangements to solve problems. The authors first demonstrate the features of the arrangement package and related packages using small example programs. They then describe applications, i.e., complete standalone programs written on top of CGAL arrangements used to solve meaningful problems – for example, finding the minimum-area triangle defined by a set of points, planning the motion of a polygon translating among polygons in the plane, computing the offset polygon, finding the largest common point sets under approximate congruence, constructing the farthest-point Voronoi diagram, coordinating the motion of two discs moving among obstacles in the plane, and performing Boolean operations on curved polygons. The book contains comprehensive explanations of the solution programs, many illustrations, and detailed notes on further reading, and it is supported by a website that contains downloadable software and exercises. It will be suitable for graduate students and researchers involved in applied research in computational geometry, and for professionals who require worked-out solutions to real-life geometric problems. It is assumed that the reader is familiar with the C++ programming-language and with the basics of the generic-programming paradigm.
Author: András Frank
Publisher: OUP Oxford
ISBN: 0199205272
Category : Mathematics
Languages : en
Pages : 664
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Book Description
Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.
Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 408
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Book Description
