Overview
- Very elementary introduction to the topic
- Book was developed from a lecture course at the top-level Faculty of Mathematics, Higher School of Economics
- Very student-friendly
Part of the book series: Moscow Lectures (ML, volume 10)
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About this book
This book is devoted to combinatorial aspects of the theory of symmetric functions. This rich, interesting and highly nontrivial part of algebraic combinatorics has numerous applications to algebraic geometry, topology, representation theory and other areas of mathematics. Along with classical material, such as Schur polynomials and Young diagrams, less standard subjects are also covered, including Schubert polynomials and Danilov–Koshevoy arrays. Requiring only standard prerequisites in algebra and discrete mathematics, the book will be accessible to undergraduate students and can serve as a basis for a semester-long course. It contains more than a hundred exercises of various difficulty, with hints and solutions. Primarily aimed at undergraduate and graduate students, it will also be of interest to anyone who wishes to learn more about modern algebraic combinatorics and its usage in other areas of mathematics.
Keywords
Table of contents (16 chapters)
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Front Matter
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Schur Polynomials and Young Tableaux
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Front Matter
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Arrays and the Littlewood–Richardson Rule
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Front Matter
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Schubert Polynomials and Pipe Dreams
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Front Matter
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Authors and Affiliations
About the authors
Anna Tutubalina completed her M.Sc. degree in Mathematical Education at HSE University, Moscow, in 2022. Prior to that, she got a B.Sc. degree in Mathematics at the same university. Now she is a Junior research fellow at the Laboratory of Algebraic Geometry and its Applications at HSE University, specializing in algebraic combinatorics. She also works as a mathematical educator, teaching advanced mathematical courses and organizing various extracurricular activities for high school students.
Bibliographic Information
Book Title: Symmetric Functions: A Beginner's Course
Authors: Evgeny Smirnov, Anna Tutubalina
Series Title: Moscow Lectures
DOI: https://doi.org/10.1007/978-3-031-50341-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-50340-5Published: 08 June 2024
Softcover ISBN: 978-3-031-50343-6Due: 09 July 2024
eBook ISBN: 978-3-031-50341-2Published: 07 June 2024
Series ISSN: 2522-0314
Series E-ISSN: 2522-0322
Edition Number: 1
Number of Pages: XIII, 156
Topics: Mathematics, general