2017/11/07 by ̛İlke Çanakçı, Ilke Canakci, Ralf Schiffler +2
Computer Science · Mathematics · #05A19 #11A55 (primary) #13F60 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.CO #math.NT #msc:05A19 #msc:11A55 #msc:13F60 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1711.02461
21 pages, 7 figures, new reference to Theorem 4.1
openalex publication_date 2017/11/07 · arxiv created 2019/08/22 · arxiv updated 2019/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.