Lukas Kühne
Geometry of Flag Hilbert-Poincaré series
Flag Hilbert–Poincaré series arise in the context of local Igusa zeta functions associated to hyperplane arrangements and are connected to other seemingly different enumeration problems in algebra and geometry. We study a coarsening of these series in the case of real hyperplane arrangements by applying geometric and combinatorial tools related to their chambers. In this case, we prove that the numerators of these series are coefficient-wise bounded below by the Eulerian polynomial and equality holds if and only if all chambers are simplicial. This generalizes a recent theorem of Maglione–Voll. This is joint work with Joshua Maglione.