Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformly de Bruijn sequences and symbolic Diophantine approximation on
  fractals   Intrinsic Diophantine approximation on fractals, such as the Cantor ternary
set, was undoubtedly motivated by questions asked by K. Mahler (1984). One of
the main goals of this paper is to develop and utilize the theory of infinite
de Bruijn sequences in order to answer closely related questions. In
particular, we prove that the set of infinite de Bruijn sequences in $k\geq 2$
letters, thought of as a set of real numbers via a decimal expansion, has
positive Hausdorff dimension. For a given $k$, these sequences bear a strong
connection to Diophantine approximation on certain fractals. In particular, the
optimality of an intrinsic Dirichlet function on these fractals with respect to
the height function defined by symbolic representations of rationals follows
from these results.

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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol