Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some actions of the 0-Hecke monoids of affine symmetric groups   There are left and right actions of the 0-Hecke monoid of the affine
symmetric group $\tilde{S}_n$ on involutions whose cycles are labeled
periodically by nonnegative integers. Using these actions we construct two
bijections, which are length-preserving in an appropriate sense, from the set
of involutions in $\tilde{S}_n$ to the set of $\mathbb{N}$-weighted matchings
in the $n$-element cycle graph. As an application, we compute a formula for the
bivariate generating function counting the involutions in $\tilde S_n$ by
length and absolute length. The 0-Hecke monoid of $\tilde{S}_n$ also acts on
involutions (without any cycle labelling) by Demazure conjugation. The atoms of
an involution $z \in \tilde{S}_n$ are the minimal length permutations $w$ which
transform the identity to $z$ under this action. We prove that the set of atoms
for an involution in $\tilde{S}_n$ is naturally a bounded, graded poset, and
give a formula for the set's minimum and maximum elements. Using these
properties, we classify the covering relations in the Bruhat order restricted
to involutions in $\tilde{S}_n$.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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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: math-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org