Wednesday, December 19, 2012

1212.4209 (Shigeki Akiyama et al.)

The computation of overlap coincidence in Taylor-Socolar substitution

Shigeki Akiyama, Jeong-Yup Lee
Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It turns out that the tiling has overlap coincidence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has a quasicrystalline structure.
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