Fixed-boundary octagonal random tilings: A combinatorial approach

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configurat ion 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 ro countin g formulas, which are directly related to questions of entropy in these sta tistical systems. Methods and tools From the field of enumerative combinato rics are used.