Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The M\"obius function of partitions with restricted block size   We study filters in the partition lattice formed by restricting to partitions
by type. The M\"obius function is determined in terms of the easier-to-compute
descent set statistics on permutations and the M\"obius function of filters in
the lattice of integer compositions. When the underlying integer partition is a
knapsack partition, the M\"obius function on integer compositions is determined
by a topological argument. In this proof the permutahedron makes a cameo
appearance.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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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: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con