**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 courses I have given at IMSc (Institute of Mathematical Science, Chennai, India) during four consecutive years from January to March, at the invitation of Amritanshu Prasad (Amri).

The mirror image of this website is here, kindly supported by The Institute of Mathematical Science (IMSc), Chennai, India.

After March 16, 2019, I may not be able to update this mirror image. Please go to the original website www.viennot.org

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 (January-March 2019)

Each course can be followed independently. There are many overlaps between the differents courses. I gave these courses 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».

These 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 Although transparencies and overhead projectors had been replaced by video-projectors, I tried to keep the spirit of the so-called «Viennotique» with handmade transparencies in color which are incorporated in the modern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.

The slides, the videos and this website form a kind of "video-book" which is in construction, even if all the slides and links to the videos of the 76 lectures are there.

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

some statistics:

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

The playlist from matsciencechannel of the 17 videos of this course is here** **

**part II:** 1800 slides and 19 videos for 18 lectures for a total of 24 hours.

The playlist from matsciencechannel of the 19 videos of this course is here

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

The playlist from matsciencechannel of the 22 videos of this course is here** **

**part IV:** 2500 slides and 19 videos for 19 lectures for a total of 26 hours

The playlist from matsciencechannel of the 19 videos of this course is here** **

Total: more than 9000 slides, 77 videos for 76 lectures for a total of 107 hours.

Of course there are many overlaps between the four parts, and some slides are sequences of figures related to a bijection. Thus the number 9000 does not reflect the number of "relevant" slides.

**last update: ****July 1, 2019**