Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bijections on two variations of noncrossing partitions   We find bijections on 2-distant noncrossing partitions, 12312-avoiding
partitions, 3-Motzkin paths, UH-free Schr{\"o}der paths and Schr{\"o}der paths
without peaks at even height. We also give a direct bijection between 2-distant
noncrossing partitions and 12312-avoiding partitions.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat