Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rich square-free words   A word w is rich if it has |w|+1 many distinct palindromic factors, including
the empty word. A word is square-free if it does not have a factor uu, where u
is a non-empty word.
  Pelantov\'a and Starosta (Discrete Math. 313 (2013)) proved that every
infinite rich word contains a square. We will give another proof for that
result. Pelantov\'a and Starosta denoted by r(n) the length of a longest rich
square-free word on an alphabet of size n. The exact value of r(n) was left as
an open question. We will give an upper and a lower bound for r(n), and make a
conjecture that our lower bound is exact.
  We will also generalize the notion of repetition threshold for a limited
class of infinite words. The repetition thresholds for episturmian and rich
words are left as an open question.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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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: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys