Snake graphs and continued fractions
Combinatorics
2019-08-23 v5 Number Theory
Abstract
This paper is a sequel to our previous work in which we found a combinatorial realization of continued fractions as quotients of the number of perfect matchings of snake graphs. We show how this realization reflects the convergents of the continued fractions as well as the Euclidean division algorithm. We apply our findings to establish results on sums of squares, palindromic continued fractions, Markov numbers and other statements in elementary number theory.
Cite
@article{arxiv.1711.02461,
title = {Snake graphs and continued fractions},
author = {Ilke Canakci and Ralf Schiffler},
journal= {arXiv preprint arXiv:1711.02461},
year = {2019}
}
Comments
21 pages, 7 figures, new reference to Theorem 4.1