Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\omega$-Lyndon words   Let $\A$ be a finite non-empty set and $\preceq $ a total order on $\A^\nats$
verifying the following lexicographic like condition: For each $n\in \nats$ and
$u, v\in \A^n,$ if $u^\omega \prec v^\omega$ then $ux\prec vy$ for all $x, y
\in \A^\nats.$ A word $x\in \A^\nats$ is called $\omega$-Lyndon if $x\prec y$
for each proper suffix $y$ of $x.$ A finite word $w\in \A^+$ is called
$\omega$-Lyndon if $w^\omega \prec v^\omega$ for each proper suffix $v$ of $w.$
In this note we prove that every infinite word may be written uniquely as a
non-increasing product of $\omega$-Lyndon words.

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: cs