Séminaire Lotharingien de Combinatoire, 93B.106 (2025), 12 pp.

Theo Douvropoulos and Olivier Bernardi

Deformations of Restricted Reflection Arrangements

Abstract. We construct free, non-constant multiplicities and free Shi-like deformations for all restrictions of Weyl arrangements A_W. Both are given in terms of root-theoretic data of W and our proofs are case-free. In type-A we give a bijective proof of resulting product formulas for the number of regions of the deformations, while at the same time proving a wide generalization of Joyal's bijection between labeled trees and functions.

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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