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Digit Sets for Self-similar Tiles

Digit Sets for Self-similar Tiles
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摘要 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. 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.
作者 Yu-Mei XUE La-na LI
机构地区 School of Mathematics and System Sciences and LMIB
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第2期493-498,共6页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China(No.11371044)
关键词 self-similar tile product-form digit set weak product-form digit set very weak product-form digit set self-similar tile product-form digit set weak product-form digit set very weak product-form digit set
分类号 O189 [理学—基础数学]
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参考文献9

  • 1Bandt, C. Self-similar Sets 5. Integer matrices and fractal tilings of . Proc. Amer. Math. Soc., 112: 549-562 (1991).
  • 2Hutchinson, J.E. Fractals and self-similarity, Indiana Univ. Math. J., 30:713-747 (1981).
  • 3Kenyon, R. Self-replicating tilings. In Symbolic dynamics and its applications, Contemporary mathematics series, (P. Walters, ed.). American Mathematical Society, Providence, RI, Vol. 135, 1992, 239-263.
  • 4Kenyon, R. Projecting the one-dimensional Sierpinski gasket. Israel j. Math., 97:221-238 (1997).
  • 5Lagarias, J.C., Wang, Y. Self-affine tiles in n. Adv. Math., 121:21-49 (1996).
  • 6Lagarias, J.C., Wang, Y. Tilings the line with translation of one tile. Invent. Math., 124(1996), 341-265 (1996).
  • 7Lagarias, J.C., Wang,Y. Integral self-affine tiles in R I. Lattice tilings. J. Fourier Anal Appl., 3:84-102 (1997).
  • 8Lau, K-S., Rao, H. On one-dimensional self-similar tilings and pq-tiles. Trans. of the AMS., 355(4): 1401-1414 (2002).
  • 9Odlyzko, A.M. Non-negative digit sets in positional number systems. Proc. London Mth. Soc., 37: 213-229 (1978).
Acta Mathematicae Applicatae Sinica
2015年 第2期

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