Parking Spaces for Complex Reflection Groups

2025/02/04 by Stack, Jason
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.01970

Abstract

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 × 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 G₃₄, E₇, and E₈.

Related

• Parking Structures: Fuss Analogs
• Parking Spaces
• On the Existence of Generalized Parking Spaces for Complex Reflection Groups
• Evidence for parking conjectures
• Extending the parking space