Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The lengths for which bicrucial square-free permutations exist   A square is a factor $S = (S_1; S_2)$ where $S_1$ and $S_2$ have the same
pattern, and a permutation is said to be square-free if it contains no
non-trivial squares. The permutation is further said to be bicrucial if every
extension to the left or right contains a square. We completely classify for
which $n$ there exists a bicrucial square-free permutation of length $n$.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg