TY - JOUR
T1 - The Poincaré-extended ab-index
AU - Dorpalen-Barry, Galen
AU - Maglione, Joshua
AU - Stump, Christian
N1 - Publisher Copyright:
© (2024), (Seminaire Lotharingien de Combinatoire). All rights reserved.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - ab-index
KW - hyperplane arrangement
KW - matroid
KW - oriented matroid
KW - poset
KW - quasisymmetric function
KW - R-labeling
UR - http://www.scopus.com/inward/record.url?scp=85212343571&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85212343571
SN - 1286-4889
JO - Seminaire Lotharingien de Combinatoire
JF - Seminaire Lotharingien de Combinatoire
IS - 91B
M1 - 4
ER -