### MA7531 Combinatorics Tool Kit

#### Course Details

**Description:**

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.

**CourseContent:**

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.

#### Course References:

TextBooks:

1. N. Alon and J.H. Spencer, The probabilistic method, Third Ed., John Wiley & Sons Inc., New Jeresey, 2008.

2. S. Jukna, Extremal combinatorics: with applications to computer science, Second Ed., Springer Verlag, Heidelberg, 2011.

ReferenceBooks:

1. Richard P Stanley, Enumerative Combinatorics - Volume 1, Springer. 2001

2. Richard P Stanley, Enumerative Combinatorics - Volume 2, Springer, 2001.

3. Introduction to combinatorial Species of Structures (lecture notes) â Bergeron et al. - (online copy available)

Prerequisite:Basic Linear algebra, basic combinatorics, familiarity with probability theory concepts.