**# playlist (click the video's upper-left icon)**

source: matsciencechannel 2017年1月20日

The website for this course is: http://coursimsc2017.xavierviennot.or...

**Contents:**

-introduction to the combinatorial theory of heaps: commutation monoids, basic definitions about heaps, equivalence commutation monoids and heaps monoids, graphs, posets and linear extension of a poset

-reminding formal power series and generating functions

-the 3 basic lemma: inversion formula and generating function for heaps, the logarithmic formula, equivalence between paths and heaps of cycles

-combinatorial proof with heaps of classical theorems in linear algebra, MacMahon master theorem

-heaps and algebraic graph theory: zeros of matching polynomials, acyclic orientations, chromatic polynomial

-heaps for a combinatorial theory of formal orthogonal polynomials and continued fractions

-interpretation of the reciprocal of the Rogers-Ramanujan identities with heaps of dimers

-fully commutative elements in Coxeter groups and Temperley-Lieb algebra

-applications to statistical physics: directed and multidirected animals, parallelogram polyominoes and Bessel functions, SOS models, hard gas models, Baxter hard hexagons model,

-application to 2D Lorentzian quantum gravity: causal triangulations.

complementary topics

- zeta function on graph and number theory

-minuscule representations of Lie algebra with operators on heaps

-basis for free partially commutative Lie algebra

-Ising model revisited with heaps of pieces

-interactions with string theory in physics

-the SAT problem in computer science revisited with heaps (from D. Knuth)

-heaps in computer science: Petri nets, aynchronous automata and Zielonka theorem

1 1:02:03 Viennot, Heaps of Pieces, Ch1a Commutations and heaps of pieces: basic definitions

2 1:11:48 Viennot, Heaps of Pieces, Ch1b Commutations and heaps of pieces: basic definitions

3 43:33 Viennot, Heaps of Pieces, Ch1c Commutations and heaps of pieces: basic definitions

4 46:21 Viennot, Heaps of Pieces, Ch 2a Generating functions for heaps of pieces

5 1:01:22 Viennot, Heaps of Pieces, Ch 2b Generating functions for heaps of pieces

6 1:24:56 Viennot, Heaps of Pieces, Ch2c Generating functions for heaps of pieces

7 1:24:31 Viennot, Heaps of Pieces, Ch 2d Generating functions for heaps of pieces

8 1:17:46 Viennot, Heaps of Pieces, Ch 3a Heaps and paths, flows and rearrangements monoids

9 1:39:43 Viennot, Heaps of Pieces, Ch 3b Heaps and paths, flows and rearrangements monoids

10 1:17:17 Viennot, Heaps of Pieces, Ch 4a Linear algebra revisited with heaps of pieces

11 1:17:43 Chapter 4b: Linear algebra revisited with heaps of pieces

12 1:10:44 Chapter 4c: Linear algebra revisited with heaps of pieces

13 1:18:28 Chapter 5a: Heaps and Graph Theory

14 1:25:04 Chapter 5b: Heaps and Graph Theory

15 1:18:29 Chapter 6a: Heaps and Coxeter groups

16 1:17:21 Chapter 6b: Heaps and Coxeter Groups

17 1:29:11 Chapter 7a: Heaps in Statistical Mechanics

18 1:22:23 Chapter 7b: Heaps and Statistical Mechanics

19 1:22:00 Chapter 7c: Heaps and Statistical Mechanics

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