Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Character polynomials for two rows and hook partitions   Representation theory of the symmetric group $\mathfrak{S}_n$ has a very
distinctive combinatorial flavor. The conjugacy classes as well as the
irreducible characters are indexed by integer partitions $\lambda \vdash n$. We
introduce class functions on $\mathfrak{S}_n$ that count the number of certain
tilings of Young diagrams. The counting interpretation gives a uniform
expression of these class functions in the ring of character polynomials, as
defined by \cite{murnaghanfirst}. A modern treatment of character polynomials
is given in \cite{orellana-zabrocki}. We prove a relation between these
combinatorial class functions in the (virtual) character ring. From this
relation, we were able to prove Goupil's generating function identity
\cite{goupil}, which can then be used to derive Rosas' formula \cite{rosas} for
Kronecker coefficients of hook shape partitions and two row partitions.

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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin