• 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

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

Foreword

Acknowledgements

Preface
Introduction
Some lectures for a wide audience

The video-book "The Art of Bijective Combinatorics" would not exists without the invitation by Amritanshu Prasad (Amri) to give 4 courses at IMSc during 4 consecutive years.
Many thanks to Amri, to the Institute of Mathematical Science (IMSc) for the invitation and to the audio technicians Gayathri and Kirubananth for the recordings.
Many thanks to the students (from CMI, IIT Madras and IMSc) and to the Professors form these Institutes for their support, encouragements in following these courses.
Special thanks to the Professors:Suresh Govindarajan (IIT Madras, Physics), K.N.Raghavan, S. Viswanath and V.S. Sunder (IMSc).
Many thanks to the Professors:  Arul Lakshminarayan (IIT Madras, Physics), Meena Mahajan (IMSc), N. Narayana (IIT Madras, Maths).
Many thanks to the students: G. Arunkumar (IMSc), Nimisha Pahuja (IISc, Bangalore) and Bishal Deb (CMI) .

Preliminary versions of these courses were given in various institutions:
Many thanks to the "Service de Physique Théorique" (SPhT), CEA Saclay, France  
Eléments de Combinatoire Algébrique (12 hours)  abstract   September-October 2007
Many thanks to Deepak Dhar for many invitations at the department of Physics, TIFR, Bombay, India
- in particular, course (12 hours) in 2010 for physicists on Part I and II
slides on the page  TIFR_2010
Many thanks to the Chennai Maths Institute (CMI), India, for the invitation in January 2010
- 3 lectures on Algebraic Combinatorics, January 2010
Many thanks to Luc Lapointe for several invitations in Chile:
 - Frutillar 2009, Summer School, Maths-Physics, 4 lectures    
 slides on the page  Frutillar_2009
- Talca 2010/2011 course on Part I, III and IV  
slides and summary on the page  Talca_2010/11
- Talca 2013/2014 course on Part II  
slides and summary on the page  Talca_2013/14
- Valparaiso 2014, workshop CIMPA, 4 lectures on Part II
slides and summary on the page  Valparaiso_2014
Many thanks to Sudhir Ghorpade for his invitation at IIT Bombay, India
- course in 2013 on Part III
slides and summary on the page IIT_Bombay_2013
Many thanks to Suresh Govindarajan for his invitation at the department of Physics, IIT Madras, India
- course in 2015 on Part I, II, III and IV
slides and summary on the page  IIT_Madras_2015
after this high speed course, it was decided an invitation for 3 years at IMSc to do again this course in more details.
Other courses or workshop related to this video-book
- ALEA 2011, Luminy, France, 2 lectures on Part III
slides and exercises on the page  ALEA_2011
- PEC (Petite Ecole de Combinatoire 2011/2012), LaBRI, Bordeaux, 15 letures on Part III 
slides and summary on the page  PetiteEcole_2011/12
Many thanks to Prof. K. Somasundaram for his invitation to give a course at Amrita Vishwa Vidyapeetham (Amrita University), Coimbatore, India
- A light version of Part I of ABjC  (16 hours), March-April 2018
Many thanks to Bill Chen for his invitation at Tianjin University, September 2019 
After the four Parts of the video-book ABjC were completed, a presentation of this video-book was given at the department of Aplied Mathematics
slides and summary of the four lectures on the page  Tianjin_2019
many thanks to Bill Chen and the Maths Department of Tianjin University for putting the 77 videos of ABjC on the Chinese chain bilibili.