Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Involution words: counting problems and connections to Schubert calculus
  for symmetric orbit closures   Involution words are variations of reduced words for involutions in Coxeter
groups, first studied under the name of "admissible sequences" by Richardson
and Springer. They are maximal chains in Richardson and Springer's weak order
on involutions. This article is the first in a series of papers on involution
words, and focuses on their enumerative properties. We define involution
analogues of several objects associated to permutations, including Rothe
diagrams, the essential set, Schubert polynomials, and Stanley symmetric
functions. These definitions have geometric interpretations for certain
intervals in the weak order on involutions. In particular, our definition of
"involution Schubert polynomials" can be viewed as a Billey-Jockusch-Stanley
type formula for cohomology class representatives of $\mathrm{O}_n$- and
$\mathrm{Sp}_{2n}$-orbit closures in the flag variety, defined inductively in
recent work of Wyser and Yong. As a special case of a more general theorem, we
show that the involution Stanley symmetric function for the longest element of
a finite symmetric group is a product of staircase-shaped Schur functions. This
implies that the number of involution words for the longest element of a finite
symmetric group is equal to the dimension of a certain irreducible
representation of a Weyl group of type $B$.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs