MA7654 Algebraic Combinatorics
Objectives: The course aims to reveal the fascinating interplay between Algebra, Combinatorics, and Graphs. It not only builds the fundamentals for students who plan to do PhD in Algebra/ Combinatorics / Graph theory and related topics, but also useful to students and researchers in other areas of science and engineering to which the methods of Algebra, Combinatorics, Graph theory may be applied.
Course Contents: Eigenvalues and Walks on graphs. Radon transform and hypercubes. Sperner property, lattices and boolean algebra. Enumeration under group actions. Ferrer's diagram, Young tableaux and Matrix Tree theorem. Applications to Electrical networks, planar graphs. Introduction to combinatorial commutative algebra.
Richard P Stanley, Algebraic Combinatorics : Walks - Trees - Tableaux and More, Springer, 2013.
A preliminary copy of the book is available from Stanley's webpage.
- Richard P Stanley, Enumerative Combinatorics - Volume 1, Springer. 2001
Richard P Stanley, Enumerative Combinatorics - Volume 2, Springer, 2001.
Combinatorial Commutative Algebra. Erza Miller and Bernd Sturmfels. Springer, 2005.
Rafael H Villarreal, Monomial Algebras, CRC Press, 2015.
R B Bapat, Graphs and Matrices, Springer, 2014.