期刊论文

Ngai, SM

英文

Discrete & Computational Geometry

0179-5376

2023

70

3

620-644

10.1007/s00454-023-00529-6

The first author is supported by the Fundamental Research Funds for the Central Universities CCNU19TS071, the National Natural Science Foundation of China Grant (12071171) and Hubei Provincial Natural Science Foundation of China (2020CFB833). The second author is supported in part by the National Natural Science Foundation of China Grant (11601403), China Scholarship Council and Hubei Provincial Natural Science Foundation of China (2019CFB602). The third author is supported in part by the National Natural Science Foundation of China Grants 12271156 and 11771136, the Hunan Province’ Hundred Talents Program, Construct Program of the Key Discipline in Hunan Province, and a Faculty Research Scholarly Pursuit Award from Georgia Southern University.

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We study self-affine tiles generated by iterated function systems consisting of affine mappings whose linear parts are defined by different matrices. We obtain an interior theorem for these tiles. We prove a tiling theorem by showing that for such a self-affine tile, there always exists a tiling set. We also obtain a more complete interior theorem for reptiles, which are tiles obtained when the matrices in the iterated function system are similarities. Our results extend some of the classical ones by Lagarias and Wang (Adv. Math. 121(1), 21–49...