Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugacy growth series for wreath product finitary symmetric groups   In recent work, Bacher and de la Harpe define and study conjugacy growth
series for finitary permutation groups. In two subsequent papers, Cotron,
Dicks, and Fleming study the congruence properties of some of these series. We
define a new family of conjugacy growth series for the finitary alternating
wreath product that are related to sums of modular forms of integer and
half-integral weights, the so-called \textit{mixed weight modular forms}. The
previous works motivate the study of congruences for these series. We prove
that congruences exist modulo powers of all primes $p \geq 5$. Furthermore, we
lay out a method for studying congruence properties for sums of mixed weight
modular forms in general.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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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: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: eess