Combinatorics and Physics: the use of heaps of pieces
Prof. Xavier Viennot
CNRS, Bordeaux, France.
29.01.03

---

Abstract

The relation between combinatorics and theoretical physics has been particularily active and fruitful in the last few years. It is classical to relate statistical physics and algebraic graph theory.

I will present more recent and less classical interactions, mostly based on the use of the notion of "heaps of pieces", giving a "geometric" and combinatorial interpretation of the algebraic notion of commutation classes of words of the so-called Cartier-Foata monoids (called trace monoids in theoretical computer science).

The combinatorial tour in this domain will include topics like directed animals, Baxter hard hexagons model, solid-on-solid model, and the so-called 2D lorentzian triangulations in quantum gravity.