Disklikeness of planar self-affine tiles
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AbstractWe consider the disklikeness of the planar self-affine tile T generated by an integral expanding matrix A and a consecutive collinear digit set D = {0, v, 2v, ⋯ , (|q|-1)v} ⊂ ℤ2. Let f(x) = x2+px+q be the characteristic polynomial of A. We show that the tile T is disklike if and only if 2|p| = |q+2|. Moreover, T is a hexagonal tile for all the cases except when p = 0, in which case T is a square tile. The proof depends on certain special devices to count the numbers of nodal points and neighbors of T and a criterion of Bandt and Wang (2001) on disklikeness. © 2007 American Mathematical Society.
All Author(s) ListLeung K.-S., Lau K.-S.
Journal nameTransactions of the American Mathematical Society
Volume Number359
Issue Number7
PublisherAmerican Mathematical Society
Place of PublicationUnited States
Pages3337 - 3355
LanguagesEnglish-United Kingdom

Last updated on 2021-17-04 at 00:09