Lectures in Algebraic Combinatorics: Young's Construction, Seminormal Representations, SL(2) Representations, Heaps, Basics on Finite Fields: Lecture Notes in Mathematics, cartea 2277
Autor Adriano M. Garsia, Ömer Eğecioğluen Limba Engleză Paperback – 7 oct 2020
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.
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.
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Specificații
ISBN-13: 9783030583729
ISBN-10: 3030583724
Pagini: 232
Ilustrații: XIV, 232 p. 36 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.45 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3030583724
Pagini: 232
Ilustrații: XIV, 232 p. 36 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.45 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Cham, Switzerland
Cuprins
- Alfred Young’s Construction of the Irreducible Representations of Sn. - Young’s Seminormal Representation, Murphy Elements, and Content Evaluations. - On Finite Dimensional sl(2) Representations and an Application to Algebraic Combinatorics. - Heaps, Continued Fractions, and Orthogonal Polynomials. - Finite Fields.
Textul de pe ultima copertă
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.
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.
Caracteristici
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