| 素数下的整自仿tiles的数字集 |
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| 引用本文： | 张丽芬. 素数下的整自仿tiles的数字集[J]. 纯粹数学与应用数学, 2010, 26(2): 311-315. DOI: 10.3969/j.issn.1008-5513.2010.02.021 |
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| 作者姓名： | 张丽芬 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西,西安,710062 |
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| 摘 要： | 讨论了一维情形下有素数行列式值的整数自仿tiles,其数字集D的特征.通过比较b与p的关系得到如下结论：（i）pbD是mod p的一个完全剩余类;（ii）p｜bD=pγD0,其中γ∈N＊,D0是modp的一个完全剩余类.该结论可被推广到高维情形,加强了一些作者的结果.最后,给出与此结论相关的三个注记与例子.
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| 关 键 词： | 整自仿tile 迭代函数系 数字集 |
Digit sets of integral self-affine tiles with prime determinant |
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| ZHANG Li-fen. Digit sets of integral self-affine tiles with prime determinant[J]. Pure and Applied Mathematics, 2010, 26(2): 311-315. DOI: 10.3969/j.issn.1008-5513.2010.02.021 |
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| Authors: | ZHANG Li-fen |
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| Affiliation: | ZHANG Li-fen(College of Mathematics , Information Sicence,Shaanxi Normal University,Xi'an 710062,China) |
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| Abstract: | Under one-dimensional case, the author discusses the characteristic of digit sets of integral self-arlene tiles with prime determinant. By comparing the relation of b and p, we obtain the following result: (i) p+b D is a complete set of residues (rood p); (ii) p|b(=)D = p~γD_0,withγ∈N~* and Do is a complete set of residues (rood p). Note that this result can be generalized to higher dimensions, which improves some known results.Then three remarks and examples to be given to illustrate this result. |
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| Keywords: | integral self-affine tiles iterated function system digit set |
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