Symmetric Functions: A Beginner's Course [electronic resource] /
Smirnov, Evgeny.
Symmetric Functions: A Beginner's Course [electronic resource] / by Evgeny Smirnov, Anna Tutubalina. - 1st ed. 2024. - XIII, 156 p. online resource. - Moscow Lectures, 10 2522-0322 ; . - Moscow Lectures, 10 .
Schur Polynomials and Young Diagrams -- Arrays and the Littlewood-Richardson Rule -- Schubert Polynomials and Pipe-Dreams.
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.
9783031503412
10.1007/978-3-031-50341-2 doi
QA1-939
Symmetric Functions: A Beginner's Course [electronic resource] / by Evgeny Smirnov, Anna Tutubalina. - 1st ed. 2024. - XIII, 156 p. online resource. - Moscow Lectures, 10 2522-0322 ; . - Moscow Lectures, 10 .
Schur Polynomials and Young Diagrams -- Arrays and the Littlewood-Richardson Rule -- Schubert Polynomials and Pipe-Dreams.
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.
9783031503412
10.1007/978-3-031-50341-2 doi
QA1-939