## 2018-04-06

### Commutations and Heaps of Pieces by Xavier Viennot

# 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
-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

1:02:03 Viennot, Heaps of Pieces, Ch1a Commutations and heaps of pieces: basic definitions
1:11:48 Viennot, Heaps of Pieces, Ch1b Commutations and heaps of pieces: basic definitions
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
1:01:22 Viennot, Heaps of Pieces, Ch 2b Generating functions for heaps of pieces
1:24:56 Viennot, Heaps of Pieces, Ch2c Generating functions for heaps of pieces
1:24:31 Viennot, Heaps of Pieces, Ch 2d Generating functions for heaps of pieces
1:17:46 Viennot, Heaps of Pieces, Ch 3a Heaps and paths, flows and rearrangements monoids
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