  The study of combinatorial properties of mathematical objects is a very
important research field and continued fractions have been deeply studied in
this sense. However, multidimensional continued fractions, which are a
generalization arising from an algorithm due to Jacobi, have been poorly
investigated in this sense, up to now. In this paper, we propose a
combinatorial interpretation of the convergents of multidimensional continued
fractions in terms of counting some particular tilings, generalizing some
results that hold for classical continued fractions.
