2022/09/19 by Battagliola, Michele, Murru, Nadir, Santilli, Giordano
#05A10 #11A55 #11Y65 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2209.08875
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.