Combinatorics Tool Kit
Lecture Schedule: Mon
Venue: HSB 266/RMN 201
Prerequisites: A good understanding of Linear algebra and basic group theory. Familiarity with probability theorey.
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.
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.
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.
- Richard P Stanley, Enumerative Combinatorics - Volume 1, Springer. 2001
Richard P Stanley, Enumerative Combinatorics - Volume 2, Springer, 2001.
Thanks must go to my friend Amri from whose page I stole the template.