Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bruhat order, smooth Schubert varieties, and hyperplane arrangements   The aim of this article is to link Schubert varieties in the flag manifold
with hyperplane arrangements. For a permutation, we construct a certain
graphical hyperplane arrangement. We show that the generating function for
regions of this arrangement coincides with the Poincare polynomial of the
corresponding Schubert variety if and only if the Schubert variety is smooth.
We give an explicit combinatorial formula for the Poincare polynomial. Our main
technical tools are chordal graphs and perfect elimination orderings.

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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: nlin