Download or read book Arrangements of Hyperplanes written by Peter Orlik and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.
Download or read book Hyperplane Arrangements written by Alexandru Dimca and published by Springer. This book was released on 2017-03-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties. The topics discussed in this book range from elementary combinatorics and discrete geometry to more advanced material on mixed Hodge structures, logarithmic connections and Milnor fibrations. The author covers a lot of ground in a relatively short amount of space, with a focus on defining concepts carefully and giving proofs of theorems in detail where needed. Including a number of surprising results and tantalizing open problems, this timely book also serves to acquaint the reader with the rapidly expanding literature on the subject. Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.
Download or read book Topics in Hyperplane Arrangements written by Marcelo Aguiar and published by American Mathematical Soc.. This book was released on 2017-11-22 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.
Download or read book Geometric Combinatorics written by Ezra Miller and published by American Mathematical Soc.. This book was released on 2007 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Essays in honor of Gian Carlo Rota written by Bruce Sagan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In April of 1996 an array of mathematicians converged on Cambridge, Massachusetts, for the Rotafest and Umbral Calculus Workshop, two con ferences celebrating Gian-Carlo Rota's 64th birthday. It seemed appropriate when feting one of the world's great combinatorialists to have the anniversary be a power of 2 rather than the more mundane 65. The over seventy-five par ticipants included Rota's doctoral students, coauthors, and other colleagues from more than a dozen countries. As a further testament to the breadth and depth of his influence, the lectures ranged over a wide variety of topics from invariant theory to algebraic topology. This volume is a collection of articles written in Rota's honor. Some of them were presented at the Rotafest and Umbral Workshop while others were written especially for this Festschrift. We will say a little about each paper and point out how they are connected with the mathematical contributions of Rota himself.
Download or read book Facing up to Arrangements Face Count Formulas for Partitions of Space by Hyperplanes written by Thomas Zaslavsky and published by American Mathematical Soc.. This book was released on 1975 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: An arrangement of hyperplanes of Euclidean or projective d-space is a finite set of hyperplanes, together with the induced partition of the space. Given the hyperplanes of an arrangement, how can the faces of the induced partition be counted? Heretofore this question has been answered for the plane, Euclidean 3-space, hyperplanes in general position, and the d-faces of the hyperplanes through the origin in Euclidean space. In each case the numbers of k-faces depend only on the incidences between intersections of the hyperplane, even though arrangements with the same intersection incidence pattern are not in general combinatorially isomorphic. We generalize this fact by demonstrating formulas for the numbers of k-faces of all Euclidean and projective arrangements, and the numbers of bounded k-faces of the former, as functions of the (semi)lattice of intersections of the hyperplanes, not dependent on the arrangement's combinatorial type.
Download or read book Introduction to Arrangements written by Peter Orlik and published by American Mathematical Soc.. This book was released on 1989 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: An arrangement of hyperplanes is a finite collection of codimension one subspaces in a finite-dimensional vector space. Arrangements occur in several branches of mathematics: combinatorics, braids, hypergeometric functions, reflection groups, singularities, and coding theory. This book, based on lectures presented by the author at the CBMS Regional Conference held at Northern Arizona University in June 1988, provides the first introduction to the study of the topology of the complement of an arrangement in a complex vector space. The author discusses basic combinatorial tools, as well as algebras associated to the arrangement, differential forms, the cohomology and the homotopy type of the complement, free arrangements, and reflection arrangements. With a particular emphasis on topological aspects, this book provides an excellent introduction to current activity in this area.
Download or read book Lectures on Discrete Geometry written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Download or read book Convex Polytopes written by Branko Grünbaum and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London
Download or read book Arrangements of Hyperplanes written by Branko Grünbaum and published by . This book was released on 1971 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oriented Matroids written by Anders Björner and published by Cambridge University Press. This book was released on 1999-11-18 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.
Download or read book Algorithms in Combinatorial Geometry written by Herbert Edelsbrunner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Software ICMS 2020 written by Anna Maria Bigatti and published by Springer Nature. This book was released on 2020-07-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 7th International Conference on Mathematical Software, ICMS 2020, held in Braunschweig, Germany, in July 2020. The 48 papers included in this volume were carefully reviewed and selected from 58 submissions. The program of the 2020 meeting consisted of 20 topical sessions, each of which providing an overview of the challenges, achievements and progress in a environment of mathematical software research, development and use.
Download or read book Handbook of Discrete and Computational Geometry written by Csaba D. Toth and published by CRC Press. This book was released on 2017-11-22 with total page 2879 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Download or read book Perspectives in Lie Theory written by Filippo Callegaro and published by Springer. This book was released on 2017-12-07 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
Download or read book High Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
