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  1. Home > Articles & Issues >
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  3. Determining pure dis ...
Article

Determining pure discrete spectrum for some self-affine tilings

Shigeki Akiyama ORCID (1), Franz Gähler (2), Jeong-Yup Lee (3)
(1) Institute of Mathematics, University of Tsukuba
(2) Fakultät für Mathematik = Faculty of Mathematics [Bielefeld]
(3) Department of Mathematics Education [Kwandong]
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Imported on
April 3, 2014
Published on
December 15, 2014
Last modified on
March 31, 2025
Volume 16
vol. 16:3
Discrete Algorithms
DOI
10.46298/dmtcs.2089
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https://about.hal.science/hal-authorisation-v1
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Determining pure discrete spectrum for some self-affine tilings

Shigeki Akiyama ORCID (1), Franz Gähler (2), Jeong-Yup Lee (3)
(1) Institute of Mathematics, University of Tsukuba
(2) Fakultät für Mathematik = Faculty of Mathematics [Bielefeld]
(3) Department of Mathematics Education [Kwandong]
Abstract
By the algorithm implemented in the paper by Akiyama-Lee [Adv. Math. 226(4):2855 13;2883, 2011] and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to 2, and some cases of planar tilings generated by boundary substitutions due to Kenyon [Geom. Func. Anal. 6:471 13;488, 1996].
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Pisot substitution
  • pure discrete spectrum
  • self-affine tiling
Cited by

Source: OpenCitations

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