Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sets, Lists and Noncrossing Partitions   Partitions of [n]={1,2,...,n} into sets of lists are counted by sequence
number A000262 in the On-Line Encyclopedia of Integer Sequences. They are
somewhat less numerous than partitions of [n] into lists of sets, A000670. Here
we observe that the former are actually equinumerous with partitions of [n]
into lists of *noncrossing* sets and give a bijective proof. We show that
partitions of [n] into sets of noncrossing lists are counted by A088368 and
generalize this result to introduce a transform on integer sequences that we
dub the "noncrossing partition" transform. We also derive recurrence relations
to count partitions of [n] into lists of noncrossing lists.

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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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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: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an