Reidemeister spectra of free nilpotent groups and plethysms of Schur functions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912177911234560 |
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| author | Senden, Pieter |
| author_facet | Senden, Pieter |
| contents | We establish a strong link between two open problems: determining the Reidemeister spectrum of free nilpotent groups and determining the coefficients in the Schur expansion of plethysms of Schur functions. Specifically, we show that the expressions occurring in the computations for the Reidemeister spectrum are sums of plethysms of the form $s_{1^{i}}[g]$, where $g$ is a Schur function or a Schur positive function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reidemeister spectra of free nilpotent groups and plethysms of Schur functions Senden, Pieter Group Theory Combinatorics 20E36, 05E05 (Primary) We establish a strong link between two open problems: determining the Reidemeister spectrum of free nilpotent groups and determining the coefficients in the Schur expansion of plethysms of Schur functions. Specifically, we show that the expressions occurring in the computations for the Reidemeister spectrum are sums of plethysms of the form $s_{1^{i}}[g]$, where $g$ is a Schur function or a Schur positive function. |
| title | Reidemeister spectra of free nilpotent groups and plethysms of Schur functions |
| topic | Group Theory Combinatorics 20E36, 05E05 (Primary) |
| url | https://arxiv.org/abs/2501.02591 |