Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Involutions on Baxter Objects   Baxter numbers are known to count several families of combinatorial objects,
all of which come equipped with natural involutions. In this paper, we add a
combinatorial family to the list, and show that the known bijections between
these objects respect these involutions. We also give a formula for the number
of objects fixed under this involution, showing that it is an instance of
Stembridge's "$q=-1$ phenomenon".

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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol