Digit sets for self-similar tiles

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• 作者：Yu-Mei Xue ; La-na Li
• 关键词：self ; similar tile ; product ; form digit set ; weak product ; form digit set ; very weak product ; form digit set ; 11B75 ; 52C20
• 刊名：Acta Mathematicae Applicatae Sinica, English Series
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：31
• 期：2
• 页码：493-498
• 全文大小：195 KB
• 参考文献：[1]Bandt, C. Self-similar Sets 5. Integer matrices and fractal tilings of 鈩?sup>n. Proc. Amer. Math. Soc., 112: 549鈥?62 (1991)MATH MathSciNet
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  [5]Lagarias, J.C., Wang, Y. Self-affine tiles in 鈩?sup>n. Adv. Math., 121: 21鈥?9 (1996)MATH MathSciNet View Article
  [6]Lagarias, J.C., Wang, Y. Tilings the line with translation of one tile. Invent. Math., 124(1996), 341鈥?65 (1996)MATH MathSciNet View Article
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  [8]Lau, K-S., Rao, H. On one-dimensional self-similar tilings and pq-tiles. Trans. of the AMS., 355(4): 1401鈥?414 (2002)MathSciNet View Article
  [9]Odlyzko, A.M. Non-negative digit sets in positional number systems. Proc. London Math. Soc., 37: 213鈥?29 (1978)MATH MathSciNet View Article
  
• 作者单位：Yu-Mei Xue (1)
  La-na Li (1)
  
  1. School of Mathematics and System Sciences and LMIB, Beihang University, Beijing, 100191, China
  
• 刊物主题：Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics;
• 出版者：Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1618-3932

文摘

A new class of digit sets, which we called very weak product-form digit sets, is introduced and it is shown that they are tile digit set for self-similar tiles. This extends previous results about product-form and weak product-form digit sets.