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- W4377866203 abstract "For a fixed nonnegative integer $u$ and positive integer $n$, we investigate the symmetric function [sum_{d|n} left(c_d(tfrac{n}{d})right)^u p_d^{tfrac{n}{d}},] where $p_n$ denotes the $n$th power sum symmetric function, and $c_d(r)$ is a Ramanujan sum, equal to the sum of the $r$th powers of all the primitive $d$th roots of unity. We establish the Schur positivity of these functions for $u=0$ and $u=1$, showing that, in each case, the associated representation of the symmetric group $mathfrak{S}_n$ decomposes into a sum of Foulkes representations, that is, representations induced from the irreducibles of the cyclic subgroup generated by the long cycle. We also conjecture Schur positivity for the case $u= 2$." @default.
- W4377866203 created "2023-05-24" @default.
- W4377866203 creator A5072366611 @default.
- W4377866203 creator A5083294700 @default.
- W4377866203 date "2023-05-19" @default.
- W4377866203 modified "2023-10-17" @default.
- W4377866203 title "Ramanujan sums and rectangular power sums" @default.
- W4377866203 doi "https://doi.org/10.48550/arxiv.2305.12007" @default.
- W4377866203 hasPublicationYear "2023" @default.
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