Forbidden Configurations In Discrete Geometry

Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108540279
Total Pages : 284 pages
Book Rating : 4.78/5 ( download)

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Download or read book Forbidden Configurations in Discrete Geometry written by David Eppstein and published by Cambridge University Press. This book was released on 2018-05-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

Author : David Eppstein
Publisher : Cambridge University Press
ISBN 13 : 1108542972
Total Pages : 242 pages
Book Rating : 4.75/5 ( download)

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Download or read book Forbidden Configurations in Discrete Geometry written by David Eppstein and published by Cambridge University Press. This book was released on 2018-05-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.

Author : Andras Bezdek
Publisher : CRC Press
ISBN 13 : 0824747615
Total Pages : 500 pages
Book Rating : 4.19/5 ( download)

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Download or read book Discrete Geometry written by Andras Bezdek and published by CRC Press. This book was released on 2003-02-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.

Author : Andras Bezdek
Publisher : CRC Press
ISBN 13 : 0203911210
Total Pages : 489 pages
Book Rating : 4.11/5 ( download)

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Download or read book Discrete Geometry written by Andras Bezdek and published by CRC Press. This book was released on 2003-02-04 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analy

Author : Karoly Bezdek
Publisher : CRC Press
ISBN 13 : 1000000338
Total Pages : 307 pages
Book Rating : 4.37/5 ( download)

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Download or read book Volumetric Discrete Geometry written by Karoly Bezdek and published by CRC Press. This book was released on 2019-04-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents methods to apply it to other geometric problems. Part I of the text consists of survey chapters of selected topics on volume and is suitable for advanced undergraduate students. Part II has chapters of selected proofs of theorems stated in Part I and is oriented for graduate level students wishing to learn about the latest research on the topic. Chapters can be studied independently from each other. Provides a list of 30 open problems to promote research Features more than 60 research exercises Ideally suited for researchers and students of combinatorics, geometry and discrete mathematics

Author : Peter Brass
Publisher : Springer Science & Business Media
ISBN 13 : 0387299297
Total Pages : 507 pages
Book Rating : 4.97/5 ( download)

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Download or read book Research Problems in Discrete Geometry written by Peter Brass and published by Springer Science & Business Media. This book was released on 2006-01-27 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Author : Achille Braquelaire
Publisher : Springer
ISBN 13 : 3540459863
Total Pages : 444 pages
Book Rating : 4.66/5 ( download)

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Download or read book Discrete Geometry for Computer Imagery written by Achille Braquelaire and published by Springer. This book was released on 2003-08-01 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Digital Geometry for Computer Imagery, DGCI 2002, held in Bordeaux, France, in April 2002.The 22 revised full papers and 13 posters presented together with 3 invited papers were carefully reviewed and selected from 67 submissions. The papers are organized in topical sections on topology, combinatorial image analysis, morphological analysis, shape representation, models for discrete geometry, segmentation and shape recognition, and applications.

Author : Jiri Patera
Publisher : American Mathematical Soc.
ISBN 13 : 0821806823
Total Pages : 303 pages
Book Rating : 4.21/5 ( download)

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Download or read book Quasicrystals and Discrete Geometry written by Jiri Patera and published by American Mathematical Soc.. This book was released on 1998 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising the proceedings of the fall 1995 semester program arranged by The Fields Institute at the U. of Toronto, Ontario, Canada, this volume contains eleven contributions which address ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This collection of articles aims to bring into the mainstream of mathematics and mathematical physics this developing field of study integrating algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Alexander Barg
Publisher : American Mathematical Society
ISBN 13 : 1470409054
Total Pages : 202 pages
Book Rating : 4.50/5 ( download)

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Download or read book Discrete Geometry and Algebraic Combinatorics written by Alexander Barg and published by American Mathematical Society. This book was released on 2014-08-28 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.

Author : Daniel Archambault
Publisher : Springer Nature
ISBN 13 : 303035802X
Total Pages : 624 pages
Book Rating : 4.20/5 ( download)

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Download or read book Graph Drawing and Network Visualization written by Daniel Archambault and published by Springer Nature. This book was released on 2019-11-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 27th International Symposium on Graph Drawing and Network Visualization, GD 2019, held in Prague, Czech Republic, in September 2019. The 42 papers and 12 posters presented in this volume were carefully reviewed and selected from 113 submissions. They were organized into the following topical sections: Cartograms and Intersection Graphs, Geometric Graph Theory, Clustering, Quality Metrics, Arrangements, A Low Number of Crossings, Best Paper in Track 1, Morphing and Planarity, Parameterized Complexity, Collinearities, Topological Graph Theory, Best Paper in Track 2, Level Planarity, Graph Drawing Contest Report, and Poster Abstracts.