# Character polynomials for two rows and hook partitions

@article{Ashraf2018CharacterPF, title={Character polynomials for two rows and hook partitions}, author={Ahmed Umer Ashraf}, journal={arXiv: Combinatorics}, year={2018} }

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…

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