Combinatorics Tool Kit

Instructor: Narayanan N

Lecture Schedule: Mon
Tuesday
Venue: HSB 266/RMN 201

Prerequisites: A good understanding of Linear algebra and basic group theory. Familiarity with probability theorey.
Course Info:

Objectives:

The course aims to equip the students with commonly used algebraic and probabilistic tools in Combinatorics, and Graph Theory. 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 and Probability may be applied.

Course Contents:

The Twelve Fold way, Techniques from Probabilistic Method , The Method of Linear Algebra , LGV Lemma and applications, Chip firing games. Discharging method for graphs, Combinatorial Nullstellensatz, Polynomial method. Bijective combinatorics and the Catalan garden, Species of Combinatorial structures.

Text Books:

Probabilistic Method - Alon and Spencer. Volume 3, 2008.
Extremal combinatorics – Jukna, Stasis. Springer, 2011.
Richard P Stanley, Algebraic Combinatorics : Walks - Trees - Tableaux and More, Springer, 2013. A preliminary copy of the book is available from this page.

Reference Books:

  1. Richard P Stanley, Enumerative Combinatorics - Volume 1, Springer. 2001
  2. Richard P Stanley, Enumerative Combinatorics - Volume 2, Springer, 2001.
    3. Thanks must go to my friend Amri from whose page I stole the template.