Higher combinatorics

proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1-10, 1976

Author: Martin Aigner

Publisher: Springer


Category: Mathematics

Page: 256

View: 4007

Higher Combinatorics

Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1–10, 1976

Author: M. Aigner

Publisher: Springer Science & Business Media

ISBN: 9401012202

Category: Mathematics

Page: 256

View: 8688

It is general consensus that Combinatorics has developed into a full-fledged mathematical discipline whose beginnings as a charming pastime have long since been left behind and whose great signifi cance for other branches of both pure and applied mathematics is only beginning to be realized. The last ten years have witnessed a tremendous outburst of activity both in relatively new fields such as Coding Theory and the Theory of Matroids as well as in' more time honored endeavors such as Generating Functions and the Inver sion Calculus. Although the number of text books on these subjects is slowly increasing, there is also a great need for up-to-date surveys of the main lines of research designed to aid the beginner and serve as a reference for the expert. It was the aim of the Advanced Study Institute "Higher Combinatorics" in Berlin, 1976, to help fulfill this need. There were five sections: I. Counting Theory, II. Combinatorial Set Theory and Order Theory, III. Matroids, IV. Designs and V. Groups and Coding Theory, with three principal lecturers in each section. Expanded versions of most lectures form the contents of this book. The Institute was designed to offer, especially to young researchers, a comprehen sive picture of the most interesting developments currently under way. It is hoped that these proceedings will serve the same purpose for a wider audience.

Enumerative Combinatorics:

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN: 1107015421

Category: Mathematics

Page: 626

View: 6402

"Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets"--

Lectures on Advances in Combinatorics

Author: Rudolf Ahlswede,Vladimir Blinovsky

Publisher: Springer Science & Business Media

ISBN: 9783540786023

Category: Mathematics

Page: 318

View: 3556

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

Connections Between Algebra, Combinatorics, and Geometry

Author: Susan M. Cooper,Sean Sather-Wagstaff

Publisher: Springer

ISBN: 1493906267

Category: Mathematics

Page: 317

View: 9619

Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

Mappings of Operator Algebras

proceedings of the [fourth] Japan-U.S. Joint Seminar [on Operator Algebras], University of Pennsylvania, [from May 23 through May 27] 1988

Author: Araki, Takeo

Publisher: Springer Science & Business Media

ISBN: 9780817634766

Category: Mathematics

Page: 307

View: 9245

Computing and Combinatorics

First Annual International Conference, COCOON '95, Xi'an, China, August 24-26, 1995. Proceedings

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

ISBN: 9783540602163

Category: Computers

Page: 654

View: 4895

This book constitutes the proceedings of the First Annual International Conference on Computing and Combinatorics, COCOON '95, held in Xi'an, China in August 1995. The 52 thoroughly refereed full papers and the 22 short presentations included in this volume were selected from a total of 120 submissions. All current aspects of theoretical computer science and combinatorial mathematics related to computing are addressed; in particular, there are sections on complexity theory, graph drawing, computational geometry, databases, graph algorithms, distributed programming and logic, combinatorics, machine models, combinatorial designs, algorithmic learning, algorithms, distributed computing, and scheduling.

Mathematical Combinatorics, Vol. 3/2010

international book series

Author: Linfan Mao

Publisher: Infinite Study

ISBN: 1599731304


Page: N.A

View: 6763

The Mathematical Combinatorics (International Book Series)(ISBN 978-1-59973-146-9) is a fully refereed international book series, sponsored by the MADISof Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pagesapprox. per volume, which publishes original research papers and survey articles in all aspectsof Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics,non-euclidean geometry and topology and their applications to other sciences. Topics in detailto be covered are:Smarandache multi-spaces with applications to other sciences, such as those of algebraicmulti-systems, multi-metric spaces,· · · , etc.. Smarandache geometries;Differential Geometry; Geometry on manifolds;Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph andmap enumeration; Combinatorial designs; Combinatorial enumeration;Low Dimensional Topology; Differential Topology; Topology of Manifolds;Geometrical aspects of Mathematical Physics and Relations with Manifold Topology;Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatoricsto mathematics and theoretical physics;Mathematical theory on gravitational fields; Mathematical theory on parallel universes;Other applications of Smarandache multi-space and combinatorics.Generally, papers on mathematics with its applications not including in above topics arealso welcome.

Combinatorics: Ancient & Modern

Author: Robin Wilson,John J. Watkins

Publisher: OUP Oxford

ISBN: 0191630632

Category: Mathematics

Page: 392

View: 4290

Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

The Higher Infinite

Large Cardinals in Set Theory from Their Beginnings

Author: Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 3540888667

Category: Mathematics

Page: 538

View: 2655

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

Physical Combinatorics

Author: 正樹·柏原,Tetsuji Miwa

Publisher: Springer Science & Business Media

ISBN: 9780817641757

Category: Mathematics

Page: 317

View: 8989

"Taking into account the various criss-crossing among mathematical subjects, Physical Combinatorics presents new results and exciting ideas from three viewpoints: representation theory, integrable models, and combinatorics." "This volume will be of interest to mathematical physicists and graduate students in the above-mentioned fields."--BOOK JACKET.

Surveys in Combinatorics, 1989

Invited Papers at the Twelfth British Combinatorial Conference

Author: J. Siemons

Publisher: Cambridge University Press

ISBN: 9780521378239

Category: Mathematics

Page: 217

View: 4502

Many areas of current research activity in combinatorics and its applications, including graph theory, designs and probabilistic graphs, are surveyed in lectures presented at the 12th British Combinatorial Conference.

Lectures in Geometric Combinatorics

Author: Rekha R. Thomas

Publisher: American Mathematical Soc.

ISBN: 9780821841402

Category: Mathematics

Page: 143

View: 1548

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics.The connections rely on Grobner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.

Aspects of Combinatorics

A Wide-ranging Introduction

Author: Victor Bryant

Publisher: Cambridge University Press

ISBN: 9780521429979

Category: Mathematics

Page: 266

View: 7400

Building from basics and demonstrating the relationships among the various branches of combinatorics, Victor Bryant presents the results in a straightforward way. Numerous examples and exercises including hints and solutions are included throughout and serve to lead the reader to some of the deeper results of the subject, many of which are usually excluded from introductory texts.

Advances in Combinatorics

Waterloo Workshop in Computer Algebra, W80, May 26-29, 2011

Author: Ilias S. Kotsireas,Eugene V. Zima

Publisher: Springer Science & Business Media

ISBN: 3642309798

Category: Mathematics

Page: 293

View: 4556

This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life.

Computing and Combinatorics

Third Annual International Conference, COCOON '97, Shanghai, China, August 20-22, 1997. Proceedings.

Author: China) COCOON 97 (1997 : Shanghai,Tao Jiang,International Computing and Combinatorics Conference (3rd : 1997 : Shanghai, China)

Publisher: Springer Science & Business Media

ISBN: 9783540633570

Category: Computers

Page: 522

View: 4612

The book is aimed at graduate students, researchers, engineers and physicists involved in fluid computations. An up-to-date account is given of the present state of the art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary methods. Attention is given to the difficulties arising from geometric complexity of the flow domain. Uniform accuracy for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Unified methods for compressible and incompressible flows are discussed. A treatment of the shallow-water equations is included. A basic introduction is given to efficient iterative solution methods. Many pointers are given to the current literature, facilitating further study.

Surveys in Combinatorics 1985

Invited Papers for the Tenth British Combinatorial Conference

Author: Ian Anderson

Publisher: Cambridge University Press

ISBN: 0521315247

Category: Mathematics

Page: 173

View: 4290

This volume contains the invited papers at the 1985 British Combinatorial Conference presented by several distinguished mathematicians.