Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sorting Cayley permutations with pattern-avoiding machines   Pattern avoiding machines were recently introduced by Claesson, Ferrari and
the current author to gain a better understanding of the classical
$2$-stacksort problem. In this paper we generalize these devices by allowing
permutations with repeated elements, also known as Cayley permutations. The
main result is a description of those patterns such that the corresponding set
of sortable permutations is a class. We also show a new involution on the set
of Cayley permutations, obtained by regarding a pattern-avoiding stack as an
operator. Finally, we analyze two generalizations of pop-stack sorting on
Cayley permutations. In both cases we describe sortable permutations in terms
of pattern avoidance.

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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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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: acc-phys
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The categories of this paper are: supr-con