2 citations · 2 across the 7 of their papers we have counts for
7 papers
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…
All Y-friezes come from -friezes
Ian Short, Andrei Zabolotskii
We resolve a conjecture of de Saint Germain: all Y-friezes arise from -friezes. Additionally, we give a threefold characterisation of those -friezes t…
Beyond the Laurent phenomenon
Andrei Zabolotskii
In a cluster algebra, a subset of initial cluster variables can be specialised in such a way that all elements of the resulting algebra become polynomial in the remaining variables…
Classifying integer tilings and hypertilings
Oleg Karpenkov, Ian Short, Matty van Son +1
There are two objectives to this work: to classify all tame integer tilings and to classify all tame integer hypertilings. Motivation for the first objective comes from Conway and…
Wildest -tilings
Andrei Zabolotskii
Tame SL-tilings are related to Farey graph and friezes; much less is known about wild (not tame) SL-tilings. In this note, we demonstrate SL-tilings that are maximally…
Enumerating tame friezes over
Sammy Benzaira, Ian Short, Matty van Son +1
We use a class of Farey graphs introduced by the final three authors to enumerate the tame friezes over . Using the same strategy we enumerate the tame regu…
Frieze patterns and Farey complexes
Ian Short, Matty Van Son, Andrei Zabolotskii
Frieze patterns have attracted significant attention recently, motivated by their relationship with cluster algebras. A longstanding open problem has been to provide a combinatoria…