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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2605.06739 |
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| _version_ | 1866915989925396480 |
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| author | Reynolds, Martín Gómez |
| author_facet | Reynolds, Martín Gómez |
| contents | We extend the concept of two-way forest diagrams, introduced by Belk and Brown in 2003, to represent elements of $F(n)$ as a pair of infinite, bounded $n$-ary forests together with an order-preserving bijection of the leaves. This representation allows us to develop an alternative way to compute the length of an element of $F(n)$, distinct from the formula established by Fordham and Cleary in 2009. As an application of our length formula, we re-prove the existence of dead end elements in $F(n)$ and show that their depth is always two, first proved by Wladis in 2009. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forest Diagrams and Lengths for the Generalised Thompson's Group $F(n)$ Reynolds, Martín Gómez Group Theory 20F65 We extend the concept of two-way forest diagrams, introduced by Belk and Brown in 2003, to represent elements of $F(n)$ as a pair of infinite, bounded $n$-ary forests together with an order-preserving bijection of the leaves. This representation allows us to develop an alternative way to compute the length of an element of $F(n)$, distinct from the formula established by Fordham and Cleary in 2009. As an application of our length formula, we re-prove the existence of dead end elements in $F(n)$ and show that their depth is always two, first proved by Wladis in 2009. |
| title | Forest Diagrams and Lengths for the Generalised Thompson's Group $F(n)$ |
| topic | Group Theory 20F65 |
| url | https://arxiv.org/abs/2605.06739 |