Introduction to Arrangements

Introduction to Arrangements PDF

Author: Peter Orlik

Publisher: American Mathematical Soc.

Published: 1989

Total Pages: 122

ISBN-13: 9780821889169

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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.

Hyperplane Arrangements

Hyperplane Arrangements PDF

Author: Alexandru Dimca

Publisher: Springer

Published: 2017-03-28

Total Pages: 200

ISBN-13: 3319562215

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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.

Sleeping Arrangements

Sleeping Arrangements PDF

Author: Madeleine Wickham

Publisher: Macmillan

Published: 2008-07-08

Total Pages: 304

ISBN-13: 1429926864

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Chloe needs a holiday. She's sick of making wedding dresses, her partner Philip has troubles at work, and the whole family wants a break. Her wealthy friend Gerard has offered the loan of his luxury villa in Spain--perfect. Hugh is not a happy man. His immaculate wife Amanda seems more interested in her new kitchen than in him, and he works so hard to pay for it, he barely has time for his children. Maybe he'll have a chance to bond with them on holiday. His old friend Gerard has lent them a luxury villa in Spain--perfect. Both families arrive at the villa and realize the awful truth--Gerard has double-booked. What no one else realizes is that Chloe and Hugh have a history; and as tensions rise within the two families, old passions resurface. It seems that Gerard's 'accidental' double booking may not be an accident after all...

Arrangements of Hyperplanes

Arrangements of Hyperplanes PDF

Author: Peter Orlik

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 337

ISBN-13: 3662027720

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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.

Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes

Facing up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes PDF

Author: Thomas Zaslavsky

Publisher: American Mathematical Soc.

Published: 1975

Total Pages: 116

ISBN-13: 0821818546

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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.

Institutional Arrangements for Freight Transportation Systems

Institutional Arrangements for Freight Transportation Systems PDF

Author: Cambridge Systematics

Publisher: Transportation Research Board

Published: 2009

Total Pages: 68

ISBN-13: 0309118069

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TRB's National Cooperative Freight Research Program (NCFRP) Report 2: Institutional Arrangements for Freight Transportation Systems explores successful and promising institutional arrangements designed to improve freight movement. The report examines 40 guidelines, reflecting lessons learned from existing arrangements, that are designed to help agencies and industry representatives work together to invest in and improve the freight transportation system. Appendices, consisting of a literature review, workshop material, detailed case studies, and interview guide, contained on a CD-ROM (CRP-CD-72), which accompanies the printed version of the report and is available for download as an ISO image online.

Geometric Combinatorics

Geometric Combinatorics PDF

Author: Ezra Miller

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 705

ISBN-13: 0821837362

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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.

Queer Arrangements

Queer Arrangements PDF

Author: Lisa Barg

Publisher: Wesleyan University Press

Published: 2023-10-03

Total Pages: 290

ISBN-13: 0819500658

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The legacy of Black queer composer, arranger, and pianist Billy Strayhorn (1915–1967) hovers at the edge of canonical jazz narratives. Queer Arrangements explores the ways in which Strayhorn's identity as an openly gay Black jazz musician shaped his career, including the creative roles he could assume and the dynamics between himself and his collaborators, most famously Duke Ellington, but also iconic singers such as Lena Horne and Ella Fitzgerald. This new portrait of Strayhorn combines critical, historically-situated close readings of selected recordings, scores, and performances with biography and cultural theory to pursue alternative interpretive jazz possibilities, Black queer historical routes, and sounds. By looking at jazz history through the instrument(s) of Strayhorn's queer arrangements, this book sheds new light on his music and on jazz collaboration at midcentury.

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