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.
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