School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
7-7-2023
Abstract
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. While for both settings the leading term of the tile counting function is exponential (and guided by the inflation factor), the behaviour of the second-order term is strikingly different. For the finite setting, it is known that the second term is also exponential or exponential times a polynomial. We exhibit a large family of examples where the second term is at least exponential in n divided by half-integer powers of n, where n is the number of substitution steps. In particular, we provide an identity for this discrepancy in terms of linear combinations of Catalan numbers.
Recommended Citation
Frettlöh, Dirk, Alexey Garber, and Neil Mañibo. "Catalan numbers as discrepancies for a family of substitutions on infinite alphabets." Indagationes Mathematicae (2023). https://doi.org/10.1016/j.indag.2023.06.010
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Indagationes Mathematicae
DOI
10.1016/j.indag.2023.06.010
Comments
Original published version available at https://doi.org/10.1016/j.indag.2023.06.010