** Authors:**
İBRAHİM KIRAT

** Abstract: **
Let A be an n \times n expanding matrix with integer entries
and D = \{0, d_1, ... , d_{N-1} \} \subseteq {\Bbb{Z}}^n be a set of
N distinct vectors, called an N-digit set. The unique non-empty
compact set T = T(A,D) satisfying AT = T + D is called a self-affine
set. If T has positive Lebesgue measure, it is called a self-affine
region. In general, it is not clear how to determine a point to be on
the boundary of a self-affine region. In this note, we consider
one-dimensional self-affine regions T and present a simple approach to
get increasing subsets of the boundary of T. This approach also gives
a characterization of strict product-form digit sets introduced by
Odlyzko.

** Keywords: **
Self-affine sets, boundary points, strict product-form
digits

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