• XAVIER VIENNOT
  • Foreword
    • Preface
    • Introduction
    • Acknowledgements
    • Lectures for wide audience
  • PART I
    • Preface
    • Abstract
    • Contents
    • Ch0 Introduction to the course
    • Ch1 Ordinary generating functions
    • Ch2 The Catalan garden
    • Ch3 Exponential structures and genarating functions
    • Ch4 The n! garden
    • Ch5 Tilings, determinants and non-intersecting paths
    • Lectures related to the course
    • List of bijections
    • Index
  • PART II
    • Preface
    • Abstract
    • Contents
    • Ch1 Commutations and heaps of pieces: basic definitions
    • Ch2 Generating functions of heaps of pieces
    • Ch3 Heaps and paths, flows and rearrangements monoids
    • Ch4 Linear algebra revisited with heaps of pieces
    • Ch5 Heaps and algebraic graph theory
    • Ch6 Heaps and Coxeter groups
    • Ch7 Heaps in statistical mechanics
    • Lectures related to the course
  • PART III
    • Preface
    • Abstract
    • Contents
    • Ch0 overview of the course
    • Ch1 RSK The Robinson-Schensted-Knuth correspondence
    • Ch2 Quadratic algebra, Q-tableaux and planar automata
    • Ch3 Tableaux for the PASEP quadratic algebra
    • Ch4 Trees and tableaux
    • Ch5 Tableaux and orthogonal polynomials
    • Ch6 Extensions: tableaux for the 2-PASEP quadratic algebra
    • Lectures related to the course
    • References, comments and historical notes
  • PART IV
    • Preface
    • Introduction
    • Contents
    • Ch0 Overview of the course
    • Ch1 Paths and moments
    • Ch2 Moments and histories
    • Ch3 Continued fractions
    • Ch4 Computation of the coefficients b(k) lambda(k)
    • Ch5 Orthogonality and exponential structures
    • Ch6 q-analogues
    • Lectures related to the course
    • Complements
    • References
  • Epilogue

The Art of Bijective Combinatorics   Part I
An introduction to enumerative, algebraic and bijective combinatorics

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

Preface

This website is devoted to the combinatorial course I gave at IMSc (Institute of Mathematical Science), Chennai, India, in January-March 2016. The whole slides and videos of the course are available (2024 slides and 17 videos for 17 lectures, for a total of almost 24 hours). The course was 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.
I gave the course at two different levels at the same time. Most of the course is supposed to be followed by undergraduate students (at the Master level). 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 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.
Warm thanks to colleagues and friends: Amritanshu Prasand (Amri) who invited me to give this combinatorics course at IMSc, Suresh Govindarajan, Arul Lakshminarayan, V.S.Sunders, Meena Mahajan and N. Narayanan, for their support, enthusiasm, and interest in the course. Many thanks to the students from IMSc, CMI and IIT for their endurance and interest for the course and to the technicians of IMSc for making the videos. Special thanks to Sridhar, Varsha, Jinu for writing the forthcoming notes from the course.
How to quote this video-book in the literature
The videos, slides and the address of this video-book ABjC will remain unchanged. It is possible to quote this video-book in the literature in the same way as quoting a book.  If you give only the direct link to a set of slides, or to the YouTube address of a video, the reader will miss the corresponding page giving the precise decription of the slides, video and direct links in order to navigate inside the video. Also think of our Chinese colleagues, for which the link to the video is only through the popular Chinese chain "bilibili".
 I suggest the following:
-     if you want to quote one of the four part (volume) of ABjC, I suggest to quote in an analogous way to a book, with the editor (here IMSc), the place of edition (here Chennai) and the year, for example for the second volume:
The Art of Bijective Combinatorics, Part II, Commutations and heaps of pieces, IMSc, Chennai, 2017, http://www.viennot.org/abjc2.html
the suffix /abjcn.html refers to Part "N" of ABjC and the pointer goes to the web page "Preface" of Part "N"
-     if you want to quote a precise point inside the video-book, as for example a definition, theorem or bijection, I suggest to refer to the number(s) of the corresponding slide(s). Example:  the "Tamil bijection" is introduced in
The Art of Bijective Combinatorics, Part III, The cellular ansatz:  bijective combinatorics and quadratic algebra, Chapter 4c,  IMSc, Chennai, 2019, p 178, http://www.viennot.org/abjc3-ch4.html
the suffix abjc3-ch4.html refers to the web page of Chapter 4 of Part "III", this page containing the different slides and videos of the 3 lectures Ch4a, Ch4b, Ch4c corresponding to this Chapter 4.
 -     if you want to quote the whole collection of the 4 volumes then:
The Art of Bijective Combinatorics, IMSc, Chennai, 2016-2019, http://www.viennot.org/abjc.html
the suffix /abjc.html refers to the web page of the general preface of ABjC.
Xavier Viennot
email: first name (at) name (dot) org