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arXiv · 2509.17838

Twisted aughts of alternating involutions

Raghavendra N. Bhat·Cristian Cobeli·Shuta Iwai·Zimeng Ye·Alexandru Zaharescu
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Abstract

Let $\mathcal{M}(n)$ be the subgroup of $GL(n,\mathbb{Z})$ generated by the particular involutions that are identical to the identity, except for a single line where $-1$ and $+1$ alternate. We study the properties of $\mathcal{M}(n)$, and then find several notable characteristics of the unions of trajectories obtained by iteratively applying a fixed sequence of such involutions to elements from $\mathbb{Z}^n$.

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Raghavendra N. Bhat, Cristian Cobeli, Shuta Iwai, Zimeng Ye, Alexandru Zaharescu. 2025-09-22. Twisted aughts of alternating involutions. https://arxiv.org/abs/2509.17838

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