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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.18090 |
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| _version_ | 1866914280191819776 |
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| author | Adams, Anthony Dorsam, Joshua Levitsky, Lily Mann, Megan |
| author_facet | Adams, Anthony Dorsam, Joshua Levitsky, Lily Mann, Megan |
| contents | Armstrong, Reiner, and Rhoades defined for all Weyl groups $W$ a natural representation of $W$ called the $W$-parking space. The type $B$ parking space is the representation $\mathbb{C}[(\mathbb{Z}/(2n+1)\mathbb{Z})^n]$ of the $n$th signed symmetric group. We consider more general representations of the form $\mathbb{C}[(\mathbb{Z}/m\mathbb{Z})^n]$; we conjecture that this representation extends to the $(n+1)$th signed symmetric group for all $n$ and $m$. We prove this conjecture when $m = 3$ or when $n \leq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Extending Type $B$ Parking Spaces Adams, Anthony Dorsam, Joshua Levitsky, Lily Mann, Megan Combinatorics Armstrong, Reiner, and Rhoades defined for all Weyl groups $W$ a natural representation of $W$ called the $W$-parking space. The type $B$ parking space is the representation $\mathbb{C}[(\mathbb{Z}/(2n+1)\mathbb{Z})^n]$ of the $n$th signed symmetric group. We consider more general representations of the form $\mathbb{C}[(\mathbb{Z}/m\mathbb{Z})^n]$; we conjecture that this representation extends to the $(n+1)$th signed symmetric group for all $n$ and $m$. We prove this conjecture when $m = 3$ or when $n \leq 2$. |
| title | On Extending Type $B$ Parking Spaces |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.18090 |