Snake graphs and continued fractions

İlke Çanakçı, Ralf Schiffler

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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.

Original languageEnglish
Article number103081
Pages (from-to)1-19
Number of pages19
JournalEuropean Journal of Combinatorics
Volume86
Early online date30 Jan 2020
DOIs
Publication statusPublished - 1 May 2020

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