Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: (2+2)-free posets, ascent sequences and pattern avoiding permutations   We present bijections between four classes of combinatorial objects. Two of
them, the class of unlabeled (2+2)-free posets and a certain class of
involutions (or chord diagrams), already appeared in the literature, but were
apparently not known to be equinumerous. We present a direct bijection between
them. The third class is a family of permutations defined in terms of a new
type of pattern. An attractive property of these patterns is that, like
classical patterns, they are closed under the action of $D_8$, the symmetry
group of the square. The fourth class is formed by certain integer sequences,
called ascent sequences, which have a simple recursive structure and are shown
to encode (2+2)-free posets and permutations. Our bijections preserve numerous
statistics.
  We determine the generating function of these classes of objects, thus
recovering a non-D-finite series obtained by Zagier for the class of chord
diagrams. Finally, we characterize the ascent sequences that correspond to
permutations avoiding the barred pattern $3{\bar 1}52{\bar 4}$ and use this to
enumerate those permutations, thereby settling a conjecture of Pudwell.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: q-fin