3 papers
math.CO2026
Optimal local convergence criteria for integer and Gaussian integer continued fractions
Ian Short, Margaret Stanier, Matty van Son +1
The objective of this work is to determine optimal local restrictions on the coefficients of integer and Gaussian integer continued fractions that imply convergence. We identify al…
math.CO2021
Regular coverings and parallel products of Farey maps
Margaret Stanier
We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related…
math.NT2021
Necessary and sufficient conditions for convergence of integer continued fractions
Ian Short, Margaret Stanier
Fundamental to the theory of continued fractions is the fact that every infinite continued fraction with positive integer coefficients converges; however, it is unknown precisely w…