The coarse flag Hilbert-Poincaré series of the braid arrangement

Elena Hoster, Christian Stump

Published 2024-02-29, updated 2025-02-12Version 2

The paper concerns the coarse flag Hilbert-Poincar\'e series of Maglione-Voll in the case of the braid arrangement associated to the symmetric group. We explicitly construct a companion statistic $\operatorname{ino} : \mathfrak{S}_{n+1} \times \operatorname{Sym}(n) \rightarrow \mathbb{N}$ for the descent statistic on $\operatorname{Sym}(n)$ using reverse $(P,\omega)$-partitions and quasisymmetric functions.