MA7654 Algebraic Combinatorics (modified)


Course Details

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.

Course References:

Text Books:
1. Richard P Stanley, Algebraic Combinatorics : Walks - Trees - Tableaux and More, Springer, 2013.
2. A preliminary copy of the book is available from Stanley's webpage.

Reference Books:
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.