Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Staircase diagrams and enumeration of smooth Schubert varieties   We enumerate smooth and rationally smooth Schubert varieties in the classical
finite types A, B, C, and D, extending Haiman's enumeration for type A. To do
this enumeration, we introduce a notion of staircase diagrams on a graph. These
combinatorial structures are collections of steps of irregular size, forming
interconnected staircases over the given graph. Over a Dynkin-Coxeter graph,
the set of "nearly-maximally labelled" staircase diagrams is in bijection with
the set of Schubert varieties with a complete Billey-Postnikov (BP)
decomposition. We can then use an earlier result of the authors showing that
all finite-type rationally smooth Schubert varieties have a complete BP
decomposition to finish the enumeration.

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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio