Algebraic Combinatorics And Coinvariant Spaces
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| Author | : Francois Bergeron |
| Publisher | : CRC Press |
| Total Pages | : 227 |
| Release | : 2009-07-06 |
| Genre | : Mathematics |
| ISBN | : 1439865078 |
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
| Author | : Chris Godsil |
| Publisher | : Routledge |
| Total Pages | : 368 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 1351467514 |
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.
| Author | : Hélène Barcelo |
| Publisher | : Springer |
| Total Pages | : 362 |
| Release | : 2019-01-21 |
| Genre | : Mathematics |
| ISBN | : 3030051412 |
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
| Author | : Naihuan Jing |
| Publisher | : World Scientific |
| Total Pages | : 171 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9812384464 |
Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics.This book presents articles from some of the key contributors in the area. It covers Hecke algebras, Hall algebras, the Macdonald polynomial and its deviations, and their relations with other fields.
| Author | : Louis J. Billera |
| Publisher | : Cambridge University Press |
| Total Pages | : 360 |
| Release | : 1999-09-28 |
| Genre | : Mathematics |
| ISBN | : 9780521770873 |
This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
| Author | : Eiichi Bannai |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 303 |
| Release | : 2021-02-22 |
| Genre | : Mathematics |
| ISBN | : 3110627736 |
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.
| Author | : Christopher David Godsil |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : MATHEMATICS |
| ISBN | : 9781315137131 |
"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."--Provided by publisher.
| Author | : Richard P. Stanley |
| Publisher | : Springer |
| Total Pages | : 268 |
| Release | : 2018-06-06 |
| Genre | : Mathematics |
| ISBN | : 3319771736 |
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 understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of 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, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. 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. The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added. From reviews of the first edition: “This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics ... . Stanley’s emphasis on ‘gems’ unites all this —he chooses his material to excite students and draw them into further study. ... Summing Up: Highly recommended. Upper-division undergraduates and above.” —D. V. Feldman, Choice, Vol. 51(8), April, 2014
| Author | : Zsuzsanna Lipták |
| Publisher | : Springer |
| Total Pages | : 377 |
| Release | : 2016-03-09 |
| Genre | : Computers |
| ISBN | : 3319295160 |
This book constitutes the thoroughly refereed post-workshop proceedings for the 26 International Workshop on combinatorial Algorithms, IWOCA 2015, held in Verona, Italy, in October 2015. The 29 revised full papers presented were carefully reviewed and selected from a total of 90 submissions. The topics of the papers include algorithms and data structures (including sequential, parallel, distributed, approximation, probabilistic, randomised, and on-line algorithms), algorithms on strings and graphs; applications (bioinformatics, music analysis, networking, and others); combinatorics on words; combinatorial enumeration; combinatorial optimization; complexity theory; computational biology; compression and information retrieval; cryptography and information security; decompositions and combinatorial designs; discrete and computational geometry; graph drawing and labeling; graph theory.
| Author | : Andreas Maletti |
| Publisher | : Springer |
| Total Pages | : 231 |
| Release | : 2015-09-09 |
| Genre | : Computers |
| ISBN | : 3319230212 |
This book constitutes the refereed proceedings of the 6th International Conference on Algebraic Informatics, CAI 2015, held in Stuttgart, Germany, in September 2015. The 15 revised full papers presented were carefully reviewed and selected from 25 submissions. The papers cover topics such as data models and coding theory; fundamental aspects of cryptography and security; algebraic and stochastic models of computing; logic and program modelling.
