3 papers
math.CO2024
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…
math.DS2018
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…
math.MG2018
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…