6 citations · 13 across the 8 of their papers we have counts for
8 papers
Overlapping substitutions and tilings
Shigeki Akiyama, Yasushi Nagai, Shu-Qin Zhang
We generalize the notion of (geometric) substitution rule to obtain overlapping substitutions. Our motivating example is the substitution presented in Ziherl, Dotera and Bekku \cit…
Monochromatic arithmetic progressions in automatic sequences with group structure
Ibai Aedo, Uwe Grimm, Neil Mañibo +2
We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (one-sided) fixed points of aper…
Absence of absolutely continuous diffraction spectrum for certain S-adic tilings
Yasushi Nagai
Quasiperiodic tilings are often considered as structure models of quasicrystals. In this context, it is important to study the nature of the diffraction measures for tilings. In th…
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…
A new relation between geometric and dynamical properties of objects such as tilings and Delone sets
Yasushi Nagai
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems…
The Common Structure For Objects In Aperiodic Order And The Theory Of Local Matching Topology
Yasushi Nagai
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of thes…
A General Framework for tilings, Delone sets, functions and measures, and their interrelation
Yasushi Nagai
We define a general framework that includes objects such as tilings, Delone sets, functions and measures. We define local derivability and mutual local derivability (MLD) between a…
Distribution of Patches in Tilings and Spectral Properties of Corresponding Dynamical Systems
Yasushi Nagai
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From…