Twisted aughts of alternating involutions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909799681097728 |
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| author | Bhat, Raghavendra N. Cobeli, Cristian Iwai, Shuta Ye, Zimeng Zaharescu, Alexandru |
| author_facet | Bhat, Raghavendra N. Cobeli, Cristian Iwai, Shuta Ye, Zimeng Zaharescu, Alexandru |
| contents | 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 $\mathbb{Z}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twisted aughts of alternating involutions Bhat, Raghavendra N. Cobeli, Cristian Iwai, Shuta Ye, Zimeng Zaharescu, Alexandru Number Theory Primary 11B37, Secondary 51F15, 11B50 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 $\mathbb{Z}^n$. |
| title | Twisted aughts of alternating involutions |
| topic | Number Theory Primary 11B37, Secondary 51F15, 11B50 |
| url | https://arxiv.org/abs/2509.17838 |