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math.CO2022
Catalan numbers as discrepancies for a family of substitutions on infinite alphabets
Dirk Frettlöh, Alexey Garber, Neil Mañibo
In this work, we consider a class of substitutions on infinite alphabets and show that they exhibit a growth behaviour which is impossible for substitutions on finite alphabets. Wh…
math.CO2011
Selfdual Substitutions in Dimension One
Valérie Berthé, Dirk Frettlöh, Victor Sirvent
There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselve…