Disklikeness of planar self-affine tiles |
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| Authors: | King-Shun Leung Ka-Sing Lau |
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| Affiliation: | Department of Mathematics, Science, Social Sciences and Technology, The Hong Kong Institute of Education, Tai Po, Hong Kong ; Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong |
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| Abstract: | We consider the disklikeness of the planar self-affine tile  generated by an integral expanding matrix  and a consecutive collinear digit set  . Let  be the characteristic polynomial of  . We show that the tile  is disklike if and only if  . Moreover,  is a hexagonal tile for all the cases except when  , in which case  is a square tile. The proof depends on certain special devices to count the numbers of nodal points and neighbors of  and a criterion of Bandt and Wang (2001) on disklikeness. |
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| Keywords: | Digit sets neighbors nodal points radix expansion self-affine tiles |
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