Self-Affine Tiles in Rn
نویسندگان
چکیده
A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves several results about the structure of tilings of R possible using such tiles, and gives examples showing the possible relations between self-replicating tilings and general tilings, which clarify some results of Kenyon (1992) on self-replicating tilings.
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