Journal
ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES
Volume 78, Issue -, Pages 437-451Publisher
INT UNION CRYSTALLOGRAPHY
DOI: 10.1107/S2053273322006714
Keywords
pure discrete spectrum; regular model sets; non-unimodular substitution; Pisot family substitution; Meyer sets
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Funding
- National Research Foundation of Korea [2019R1I1A3A01060365]
- National Research Foundation of Korea [2019R1I1A3A01060365] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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This paper investigates substitution tilings with pure discrete spectrum and presents their characteristics and properties, comparing them to previous studies.
Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600-610] is that unimodularity is no longer assumed in this paper.
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