Symmetric Functions: A Beginner's Course

Evgeny Smirnov is an Associate Professor of HSE University, Moscow, and the Independent University of Moscow. He obtained his Ph.D. in 2007 from the University of Grenoble, France. His main areas of interest are algebraic combinatorics and its interactions with algebraic geometry and representation theory. 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.

“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)

• Schur Polynomials and Young Diagrams.- Arrays and the Littlewood-Richardson Rule.- Schubert Polynomials and Pipe-Dreams.