Open Problems in Algebraic Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Open Problems in Algebraic Combinatorics write by Christine Berkesch. This book was released on 2024-08-21. Open Problems in Algebraic Combinatorics available in PDF, EPUB and Kindle. In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Algebraic Combinatorics
Algebraic Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Combinatorics write by Richard P. Stanley. This book was released on 2013-06-17. Algebraic Combinatorics available in PDF, EPUB and Kindle. 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.
Connections Between Algebra, Combinatorics, and Geometry
Connections Between Algebra, Combinatorics, and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Connections Between Algebra, Combinatorics, and Geometry write by Susan M. Cooper. This book was released on 2014-05-16. Connections Between Algebra, Combinatorics, and Geometry available in PDF, EPUB and Kindle. 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.
Combinatorial Commutative Algebra
Combinatorial Commutative Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combinatorial Commutative Algebra write by Ezra Miller. This book was released on 2005-06-21. Combinatorial Commutative Algebra available in PDF, EPUB and Kindle. Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Algebraic Curves over a Finite Field
Algebraic Curves over a Finite Field - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves over a Finite Field write by J. W. P. Hirschfeld. This book was released on 2013-03-25. Algebraic Curves over a Finite Field available in PDF, EPUB and Kindle. This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
