MA7654 Algebraic Combinatorics
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.
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.
1. Richard P Stanley, Enumerative Combinatorics - Volume 1, Springer. 2001
2. Richard P Stanley, Enumerative Combinatorics - Volume 2, Springer, 2001.
3. Combinatorial Commutative Algebra. Erza Miller and Bernd Sturmfels. Springer, 2005.
4. Rafael H Villarreal, Monomial Algebras, CRC Press, 2015.
5. R B Bapat, Graphs and Matrices, Springer, 2014.
A decent course in group theory and a good knowledge in linear algebra.