The self-affine property of (U,r)-Carlitz sequences of polynomials deciphered in terms of graph directed IFS

Authors:
Tian-Jia Ni;Zhi-Ying Wen
Affiliations:
Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, PR China;Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, PR China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

By defining the mth graphical representation of a (U,r)-Carlitz sequence of polynomials, we visualize the nonzero elements in a number table of coefficients of the first m polynomials. When appropriately scaled, these graphical representations are compact sets contained in a fixed closed rectangle. We established the condition under which a subsequence of these scaled graphical representations converges to a compact set with respect to the Hausdorff metric. Furthermore, under the same condition, the limit set is shown to have self-affine property which can be deciphered in terms of graph directed self-affine iterated function system (GAIFS).