Alladi Ramakrishnan Hall

The birth of a New Domain: Combinatorial Physics

Xavier Viennot

Laboratoire Bordelais de Recherche en Informatique, Bordeaux

The interaction between Combinatorics and Physics is not new: the classical combinatorial solution of the Ising model for ferromagnetism goes back to the 60’s. In the last 30 years, there has been a  renaissance of combinatorics, especialy what is called enumerative, algebraic and bijective combinatorics. Powerful combinatorial tools have been discovered, in relation with other domains of pure mathematics, and such tools appear to be useful for theoretical physics. 

With some examples I will illustrate this fruitful interaction between combinatorics and physics, giving rise to a domain which can be called ``Combinatorial Physics''. A new journal is born ``Combinatorics, Physics and their Interactions'' in the prestigious series of the Annales of Poincarré Institute in Paris. In the front page one can read: 

"The unfolding of new ideas in physics is often tied to the development of new combinatorial methods, and conversely some problems in combinatorics have been successfully attacked using methods inspired by statistical physics or quantum field theory"