Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polymatroids, closure operators and lattices   We study the closure operators of polymatroids from a lattice theoretic point
of view. We show that polymatroid closure operators relate to lattices enriched
with a generating set in the same way that matroids relate to geometric
lattices. Through this relation we define a notion of minors for lattices
enriched with a generating set. For the lattice of flats of a graphic matroid,
the minors of the lattice are shown to correspond to simple minors of the graph
when the vertices are labeled and the edges unlabeled. This correspondence is
generalized to all polymatroids.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom