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arXiv · 2006.00035

Algorithmically distinguishing irreducible characters of the symmetric group

Timothy Y. Chow·Jennifer Paulhus
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Abstract

Suppose that $\chi_\lambda$ and $\chi_\mu$ are distinct irreducible characters of the symmetric group $S_n$. We give an algorithm that, in time polynomial in $n$, constructs $\pi\in S_n$ such that $\chi_\lambda(\pi)$ is provably different from $\chi_\mu(\pi)$. In fact, we show a little more. Suppose $f=\chi_\lambda$ for some irreducible character $\chi_\lambda$ of $S_n$, but we do not know $\lambda$, and we are given only oracle access to $f$. We give an algorithm that determines $\lambda$, using a number of queries to $f$ that is polynomial in $n$. Each query can be computed in time polynomial in $n$ by someone who knows $\lambda$.

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Timothy Y. Chow, Jennifer Paulhus. 2020-05-29. Algorithmically distinguishing irreducible characters of the symmetric group. https://arxiv.org/abs/2006.00035

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