Geodesic Rosen Continued Fractions

Short, Ian and Walker, Mairi (2016). Geodesic Rosen Continued Fractions. The Quarterly Journal of Mathematics, 67(4) pp. 519–549.

DOI: https://doi.org/10.1093/qmath/haw025

Abstract

We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's original work about words in Hecke groups, and it also helps us to identify Rosen continued fraction expansions of shortest length.

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