Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinct Squares in Circular Words   A circular word, or a necklace, is an equivalence class under conjugation of
a word. A fundamental question concerning regularities in standard words is
bounding the number of distinct squares in a word of length $n$. The famous
conjecture attributed to Fraenkel and Simpson is that there are at most $n$
such distinct squares, yet the best known upper bound is $1.84n$ by Deza et al.
[Discr. Appl. Math. 180, 52-69 (2015)]. We consider a natural generalization of
this question to circular words: how many distinct squares can there be in all
cyclic rotations of a word of length $n$? We prove an upper bound of $3.14n$.
This is complemented with an infinite family of words implying a lower bound of
$1.25n$.

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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph