  Some combinatorial properties of fixed boundary rhombus random tilings with
octagonal symmetry are studied. A geometrical analysis of their configuration
space is given as well as a description in terms of discrete dynamical systems,
thus generalizing previous results on the more restricted class of
codimension-one tilings. In particular this method gives access to counting
formulas, which are directly related to questions of entropy in these
statistical systems. Methods and tools from the field of enumerative
combinatorics are used.
