Tile Digit Sets of Integral Self-affne Tilings
La-na Li · Gongcheng shuxue xuebao · 2010
Integral self-affne tilings generated by an expanding integer matrix A ∈ Mn(Z) and D ={d1,d2,...,dm} ■ Zn have been studied by many works.An important problem is to decide when a digit set gives us a tile(and then we call it a tile digit set).It is shown that the standard digit sets by Bandt,product form digit sets by Lagarias and Wang,and weak-product form digit sets in R1 by Lau and Rao are tile digit sets.In this paper,we generalize the notion of weak product form to higher dimensions and prove that they are tile digit sets.