Dorpalen-Barry-Maglione-Stump
#####
Séminaire Lotharingien de Combinatoire, 91B.4 (2024), 12 pp.

# Galen Dorpalen-Barry, Joshua Maglione and Christian Stump

# The Poincaré-extended **ab**-Index

**Abstract.**
Motivated by a conjecture concerning Igusa local zeta functions for
intersection posets of hyperplane arrangements, we introduce and study
the *Poincaré-extended* **ab**-*index*, which
generalizes both the **ab**-index and the
Poincaré polynomial. For posets admitting *R*-labelings, we give a
combinatorial description of the coefficients of the extended
**ab**-index, proving their nonnegativity.
In the case of intersection posets of hyperplane arrangements,
we prove the above conjecture of the second author and Voll.

Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.

The following versions are available: