ON FILLINGS OF 2N-GONS WITH RHOMBI

In the first part of this paper we give a generalization of a result of Ringel [11] on simple arrangements of pseudolines. In terms of fillings with rhombi of an N-zonogon, we obtain a way of generating every filling from a given one by successively performing the same local transformation. In the second part we interpret, via oriented matroids, fillings of N-zonogons with rhombi as families of vectors in Z(N). While for results in Section 1 the finiteness of the filling is essential, the aim of Section 2 is to strengthen the possibility already pointed out by Dress [7] of obtaining de Bruijn's results [4] on Penrose tilings from a purely combinatorial point of view.