**The Art of Bijective Combinatorics**

The Institute of Mathematical Sciences, Chennai, India (January-March 2016-2019)

This website "The Art of Bijective Combinatorics" is devoted to the combinatorial course I am giving at IMSc (Institute of Mathematical Science, Chennai, India) each year from January to March, at the invitation of Amritanshu Prasad (Amri).

A mirror image of this website is accessible here at IMSc. (last update17 January 2019)

This course is in four parts:

part I: An introduction to enumerative, algebraic and bijective combinatorics (January-March 2016)

part II: Commutations and heaps of pieces with interactions in physics, mathematics and computer science (January-March 2017)

part III: The cellular ansatz: bijective combinatorics and quadratic algebra (January-March 2018)

part IV: A combinatorial theory of orthogonal polynomials and continued fractions (2019)

Each course can be followed independently. There are some overlaps between the differents courses. I gave Part I and Part II of the course at two different levels at the same time. Most of the course is supposed to be followed by good undergraduate students (at the Master level) and graduate students. I also gave some more advanced topics, opening some «windows» without proof, for graduate students, researchers and professors, in connection with active researches in combinatorics, and sometimes with connection in theoretical physics and computer science. Such sections are listed under the name «Complements».

The first two courses were followed by undergraduate and graduate students, together with some professors, in mathematics, physics and computer science, from IMSc and the neighbourless institutes in Chennai: CMI (Chennai Mathematical Institute) and IIT (Indian Institute of Technology) Madras.

The emphasis of the course being on the bijective point of view in combinatorics, there are many figures and visual mathematics. Although transparencies and overhead projectors had been replaced by video-projectors, I tried to keep the spirit of the so-called «Viennotique» with handmade transparencies in color which are incorporated in the modern techniques. Each course is video-recorded (video on Youtube) and the whole slides and videos of the course are available from this website.

part I: 2000 slides and 17 videos for 17 lectures, for a total of almost 24 hours.

part II: 1800 slides and 18 videos for a total of 24 hours.

part III: 3000 slides and 22 videos for a total of 33 hours

part IV: I plan to give it in 2019.

Special thanks to The Institute of Mathematical Sciences, Chennai, to Amritanshu Prasad and the video department

**last update: 25 April 2018**