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arXiv · 1710.10063

Application of Character Estimates to the Number of $T_2$-Systems of the Alternating Group

Stefan-Christoph Virchow
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Abstract

We use character theory and character estimates to show that the number of $T_2$-systems of $A_n$ is at least \begin{equation*} \frac{1}{8n\sqrt{3}}\exp\left(\frac{2\pi}{\sqrt{6}}n^{1/2}\right)(1+o(1)). \end{equation*} Applying this result, we obtain a lower bound for the number of connected components of the product replacement graph $\Gamma_2(A_n)$.

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Stefan-Christoph Virchow. 2017-10-27. Application of Character Estimates to the Number of $T_2$-Systems of the Alternating Group. https://arxiv.org/abs/1710.10063

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