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

Some  lectures related to the course

 

Proofs without words: the example of the Ramanujan continued fraction

 abstract:

Visual proofs of identities were common at the Greek time, such as the Pythagoras theorem. In the same spirit, with the renaissance of combinatorics, visual proofs of much deeper identities become possible. Some identities can be interpreted at the combinatorial level, and the identity is a consequence of the construction a weight preserving bijection between the objects interpreting both sides of the identity.

 In this lecture, I will give an example involving the famous and classical Ramanujan continued fraction. The construction is based on the concept of "heaps of pieces",

which gives a spatial interpretation of the commutation monoids introduced by Cartier and Foata in 1969. 

 

Ramanujan Institute, Chennai, India,  10 January 2017

          Twenty Second Srinivasa Rajan Memorial Lecture

 

Amrita Vishwa Vidyapeetham, Amrita University,

              Coimbatore, 7  March 2017

 

Indian Institute of Sciences, Bangalore,  9 March 2017

        

colloquium IMSc, Chennai, February 21, 2019 (lecture related to Part IV of the ABjC course

slides (pdf, 28 Mo)    video link to YouTube  (from IMSc Matsciencechanel Playlist)

 

Zeta function on graphs revisited with the theory of heaps of pieces

ICGTA19, International Conference on Graph Theory and Applications, Amrita Vishwa Vidyapeetham Coimbatore, India, 5th January 2019

slides  (second version after the talk, pdf, 39Mo)

abstract

An identity of Euler expresses the classical Rieman zeta function as a product involving prime numbers. Following Ihara, Selberg, Hashimoto, Sunada, Bass and many others, this function has been extended to arbitrary graphs by defining a certain notion of « prime » for a graph, as some non-backtracking prime circuits. Some formulae has been given expressing the zeta function of a graph. We will revisit these expressions with the theory of heaps of pieces, initiated by the speaker, as a geometric interpretation of the so-called commutation monoids introduced by Cartier and Foata. Three basic lemma on heaps will be used: inversion lemma, logarithmic lemma and the lemma expressing paths on a graphs as a heap. A simpler version of the zeta function of a graph proposed recently by Giscard and Rochet can be interpreted as heaps of elementary circuits, in relation with MacMahon's Master theorem.

   

 

  «How to  color  a  map  with (-1)  color»

Amrita Vishwa Vidyapeetham, Amrita University,

              Coimbatore, 8  March 2017

  

               slides first part   (pdf  21 Mo)

               slides second part  (pdf  15 Mo)