Algebraic Combinatorics

Algebraic Combinatorics PDF Author: Richard P. Stanley
Publisher: Springer Science & Business Media
ISBN: 1461469988
Category : Mathematics
Languages : en
Pages : 226

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Book Description
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.

Algebraic Combinatorics

Algebraic Combinatorics PDF Author: Richard P. Stanley
Publisher: Springer Science & Business Media
ISBN: 1461469988
Category : Mathematics
Languages : en
Pages : 226

Get Book Here

Book Description
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.

Algebraic Combinatorics

Algebraic Combinatorics PDF Author: Eiichi Bannai
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110627736
Category : Mathematics
Languages : en
Pages : 303

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Book Description
This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Algebraic Combinatorics

Algebraic Combinatorics PDF Author: Chris Godsil
Publisher: Routledge
ISBN: 1351467506
Category : Mathematics
Languages : en
Pages : 382

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Book Description
This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Algebraic Combinatorics and Coinvariant Spaces

Algebraic Combinatorics and Coinvariant Spaces PDF Author: Francois Bergeron
Publisher: CRC Press
ISBN: 1439865078
Category : Mathematics
Languages : en
Pages : 227

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Book Description
Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and

Discrete Geometry and Algebraic Combinatorics

Discrete Geometry and Algebraic Combinatorics PDF Author: Alexander Barg
Publisher: American Mathematical Society
ISBN: 1470409054
Category : Mathematics
Languages : en
Pages : 202

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Book Description
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.

Combinatorial Algebraic Geometry

Combinatorial Algebraic Geometry PDF Author: Gregory G. Smith
Publisher: Springer
ISBN: 1493974866
Category : Mathematics
Languages : en
Pages : 391

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Book Description
This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Algebraic Combinatorics and Applications

Algebraic Combinatorics and Applications PDF Author: Anton Betten
Publisher: Springer Science & Business Media
ISBN: 3642594484
Category : Mathematics
Languages : en
Pages : 358

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Book Description
Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool for researchers and graduate students in discrete mathematics and theoretical computer science.

Algebraic Combinatorics and Computer Science

Algebraic Combinatorics and Computer Science PDF Author: H. Crapo
Publisher: Springer Science & Business Media
ISBN: 9788847000780
Category : Mathematics
Languages : en
Pages : 564

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Book Description
This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. Rota was one of the great thinkers of our times, innovator in both mathematics and phenomenology. I feel moved, yet touched by a sense of sadness, in presenting this volume of work, despite the fear that I may be unworthy of the task that befalls me. Rota, both the scientist and the man, was marked by a generosity that knew no bounds. His ideas opened wide the horizons of fields of research, permitting an astonishing number of students from all over the globe to become enthusiastically involved. The contagious energy with which he demonstrated his tremendous mental capacity always proved fresh and inspiring. Beyond his renown as gifted scientist, what was particularly striking in Gian-Carlo Rota was his ability to appreciate the diverse intellectual capacities of those before him and to adapt his communications accordingly. This human sense, complemented by his acute appreciation of the importance of the individual, acted as a catalyst in bringing forth the very best in each one of his students. Whosoever was fortunate enough to enjoy Gian-Carlo Rota's longstanding friendship was most enriched by the experience, both mathematically and philosophically, and had occasion to appreciate son cote de bon vivant. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota's untimely demise has bequeathed to science.

Algebraic Combinatorics

Algebraic Combinatorics PDF Author: Peter Orlik
Publisher: Springer Science & Business Media
ISBN: 3540683755
Category : Mathematics
Languages : en
Pages : 182

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Book Description
Each year since 1996 the universities of Bergen, Oslo and Trondheim have organized summer schools in Nordfjordeid in various topics in algebra and related ?elds. Nordfjordeid is the birthplace of Sophus Lie, and is a village on the western coast of Norway situated among fjords and mountains, with sp- tacularscenerywhereveryougo. AssuchitisawelcomeplaceforbothNor- gian and international participants and lecturers. The theme for the summer school in 2003 was Algebraic Combinatorics. The organizing committee c- sisted of Gunnar Fløystad and Stein Arild Strømme (Bergen), Geir Ellingsrud and Kristian Ranestad (Oslo), and Alexej Rudakov and Sverre Smalø (Tro- heim). The summer school was partly ?nanced by NorFa-Nordisk Forsker- danningsakademi. With combinatorics reaching into and playing an important part of ever more areas in mathematics, in particular algebra, algebraic combinatorics was a timely theme. The ?st lecture series “Hyperplane arrangements” was given by Peter Orlik. He came as a refugee to Norway, eighteen years old, after the insurrection in Hungary in 1956. Despite now having lived more than four decades in the United States, he impressed us by speaking ?uent Norwegian without a trace of accent. The second lecture series “Discrete Morse theory and free resolutions” was given by Volkmar Welker. These two topics ori- nate back in the second half of the nineteenth century with simple problems on arrangements of lines in the plane and Hilberts syzygy theorem.

Applied Combinatorics on Words

Applied Combinatorics on Words PDF Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521848022
Category : Computers
Languages : en
Pages : 646

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Book Description
Publisher Description