Digit Sets for Self-similar Tiles

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.

整数自仿Tiling的Tile数字集(英文)

关于由一个扩张矩阵A∈Mn(Z)和数字集D={d1,d2,...,dm}■Zn生成的整数自仿Tiling,已经有很多研究结果。其中一个重要的问题是判定一个数字集在什么条件下能生成一个Tile。在一维情况下,已知结果有:标准数字集,乘积形式数字集,弱乘积形式数字集都是Tile数字集。在本文中,我们把弱乘积形式的概念推广到高维,并证明它们都是Tile数字集。