Name
Abstract | ||
|---|---|---|
Let T be a self-affine tile that is generated by an expanding integral matrix A and a digit set D . It is known that many properties of T are invariant under the Z -similarity of the matrix A . In [LW1] Lagarias and Wang showed that if A is a 2 2 expanding matrix with |det( A )| = 2 , then the Z -similar class is uniquely determined by the characteristic polynomial of A . This is not true if |det( A )| > 2. In this paper we give complete classifications of the Z -similar classes for the cases |det( A )| =3, 4, 5 . We then make use of the classification for |det( A )| =3 to consider the digit set D of the tile and show that μ(T) >0 if and only if D is a standard digit set. This reinforces the conjecture in [LW3] on this. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1007/s00454-001-0091-2 | Discrete & Computational Geometry |
Keywords | Field | DocType |
characteristic polynomial | Affine transformation,Discrete mathematics,Characteristic polynomial,Combinatorics,Matrix (mathematics),If and only if,Invariant (mathematics),Tile,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
28 | 1 | 0179-5376 |
Citations | PageRank | References |
2 | 0.64 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ibrahim Kirat | 1 | 6 | 1.80 |
| Ka-Sing Lau | 2 | 6 | 2.48 |