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math.DS2020
Pure Discrete Spectrum and Regular Model Sets in Unimodular Substitution Tilings on R^d
Dong-il Lee, Shigeki Akiyama, Jeong-Yup Lee
We consider primitive substitution tilings on R^d whose expansion maps are unimodular. We assume that all the eigenvalues of the expansion maps are algebraic conjugates with the sa…
math.DS2020★ 6 cited
On arithmetic progressions in non-periodic self-affine tilings
Yasushi Nagai, Shigeki Akiyama, Jeong-Yup Lee
We study the repetition of patches in self-affine tilings in R^d. In particular, we study the existence and non-existence of arithmetic progressions. We first show that an arithmet…