XAVIER VIENNOT
  • PART I
    • 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
    • list of bijections
    • index
  • PART II
    • 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
    • Some lectures related to the course
  • PART III
    • 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
    • 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)

Ch 0  Introduction to the course

 

    5 January 2016

 

                               slides_Ch0     (pdf   25 Mo)             video Ch 0       (1h 10mn)

 

 

enumerative combinatorics 3    0:50    

an example with Young tableaux 5    2:08 

Hook-length formula 10    6:12  

another example with binary trees, the use of ordinary generating functions  19      9:34

an example with alternating permutations, the use of exponential generating functions 35     17:05

bijective combinatorics, example: planar maps 42    29:35

bijective proof of an identity, example RSK  48     35:10

algebraic combinatorics 55      39:50

the bijective paradigm 62    43:55

example: Mehler identity for Hermite polynomials 64    45:20

identities, bijections, « bijective tools »  84     55:41

example: hook-length formula and number of tilings of the  Aztec diagram under the same roof 89    59:33

another example: heaps of pieces 95    1:04:11

map of the course 97     1:05:31  

other courses    98     1:08:50

the end 98      1:09:52  

 

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