English

Combinatorial properties of multidimensional continued fractions

Number Theory 2022-09-20 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2209.08875,
  title  = {Combinatorial properties of multidimensional continued fractions},
  author = {Michele Battagliola and Nadir Murru and Giordano Santilli},
  journal= {arXiv preprint arXiv:2209.08875},
  year   = {2022}
}
R2 v1 2026-06-28T01:34:28.378Z