Ulteriori informazioni
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.
Sommario
Schur Polynomials and Young Diagrams.- Arrays and the Littlewood-Richardson Rule.-
Schubert Polynomials and Pipe-Dreams.
Relazione
Each chapter of the book ends with exercises, and each section includes a set of exercises that explore tangential topics related to that section. ... The general treatment in the book is somewhat brisk but offers a valuable resource as a treatment that moves toward the major combinatorial results in the theory quickly, preparing students for further study of the subject or the application of their choice. (Matthew Davis, zbMATH 1553.05003, 2025)
