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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01970 |
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| _version_ | 1866912217866174464 |
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| author | Stack, Jason |
| author_facet | Stack, Jason |
| contents | We answer an open problem of arXiv:1204.1760 and arXiv:1205.4293, extending their work to irreducible well--generated complex reflection groups $W$. We define a combinatorial $W$-noncrossing parking space and an algebraic $W$-parking space for such $W$, and exhibit a $(W \times C)$-equivariant isomorphism between the two. As a consequence of this isomorphism, we enumerate the $W$-noncrossing parking functions. Finally, we extend our results to the Fuss case. We prove the results for all such complex reflection groups except $G_{34}$, $E_7,$ and $E_8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parking Spaces for Complex Reflection Groups Stack, Jason Combinatorics We answer an open problem of arXiv:1204.1760 and arXiv:1205.4293, extending their work to irreducible well--generated complex reflection groups $W$. We define a combinatorial $W$-noncrossing parking space and an algebraic $W$-parking space for such $W$, and exhibit a $(W \times C)$-equivariant isomorphism between the two. As a consequence of this isomorphism, we enumerate the $W$-noncrossing parking functions. Finally, we extend our results to the Fuss case. We prove the results for all such complex reflection groups except $G_{34}$, $E_7,$ and $E_8$. |
| title | Parking Spaces for Complex Reflection Groups |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.01970 |