Lattice Loop Models and Combinatorics

Jean-Bernard Zuber

Abstract: I introduce the remarkable conjecture by Razumov and Stroganov connecting two very different problems: the determination of the ground state of the O(1) dense loop model on the one hand, the counting of configurations of "fully packed loops" on the other. The latter gives rise to interesting combinatorial considerations, with determinant formulae for enumeration of tilings, etc.