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2015 , Vol. 31 >Issue 2: 493 - 498

DOI: https://doi.org/10.1007/s10255-015-0481-5

论文

Digit Sets for Self-similar Tiles

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  • School of Mathematics and System Sciences and LMIB, Beihang University, Beijing 100191, China

收稿日期: 2010-09-10

  网络出版日期: 2015-04-15

基金资助

Supported by the National Natural Science Foundation of China (No. 11371044).

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Digit Sets for Self-similar Tiles

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  • School of Mathematics and System Sciences and LMIB, Beihang University, Beijing 100191, China

Received date: 2010-09-10

  Online published: 2015-04-15

Supported by

Supported by the National Natural Science Foundation of China (No. 11371044).

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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.

关键词： self-similar tile; product-form digit set; weak product-form digit set; very weak product-form digit set

本文引用格式

Yu-Mei XUE, La-na LI . Digit Sets for Self-similar Tiles[J]. 应用数学学报(英文), 2015 , 31(2) : 493 -498 . DOI: 10.1007/s10255-015-0481-5

Abstract

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.

Key words： self-similar tile; product-form digit set; weak product-form digit set; very weak product-form digit set

参考文献

[1] Bandt, C. Self-similar Sets 5. Integer matrices and fractal tilings of Rn. Proc. Amer. Math. Soc., 112: 549–562 (1991)
[2] Hutchinson, J.E. Fractals and self-similarity, Indiana Univ. Math. J., 30: 713–747 (1981)
[3] Kenyon, 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
[4] Kenyon, R. Projecting the one-dimensional Sierpinski gasket. Israel j. Math., 97: 221–238 (1997)
[5] Lagarias, J.C., Wang, Y. Self-affine tiles in Rn. Adv. Math., 121: 21–49 (1996)
[6] Lagarias, J.C., Wang, Y. Tilings the line with translation of one tile. Invent. Math., 124(1996), 341–265 (1996)
[7] Lagarias, J.C., Wang, Y. Integral self-affine tiles in Rn I. Lattice tilings. J. Fourier Anal. Appl., 3: 84–102 (1997)
[8] Lau, K-S., Rao, H. On one-dimensional self-similar tilings and pq-tiles. Trans. of the AMS., 355(4): 1401–1414 (2002)
[9] Odlyzko, A.M. Non-negative digit sets in positional number systems. Proc. London Math. Soc., 37: 213–229 (1978)

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