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}
}