Overview
- Offers an ideal supplement to a graduate level course on algebraic combinatorics
- Gives a unique take on a number of combinatorial constructs that are quite timeless
- Provides expositions which are detailed, but at the same time easily accessible, very readable, and seemingly effortless
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2277)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades.
The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability.
The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields.
The book is aimed at graduate students and researchers in the field.
Authors and Affiliations
Bibliographic Information
Book Title: Lectures in Algebraic Combinatorics
Book Subtitle: Young's Construction, Seminormal Representations, SL(2) Representations, Heaps, Basics on Finite Fields
Authors: Adriano M. Garsia, Ömer Eğecioğlu
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-58373-6
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 2020
Softcover ISBN: 978-3-030-58372-9Published: 07 October 2020
eBook ISBN: 978-3-030-58373-6Published: 06 October 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 232
Number of Illustrations: 36 b/w illustrations
Topics: Field Theory and Polynomials, Group Theory and Generalizations, Commutative Rings and Algebras