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The Poincare-Extended ab-Index

Galen Dorpalen-Barry, University of Oregon
Wednesday, April 10, 2024 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:
Galen Dorpalen-Barry
Galen Dorpalen-Barry


Motivated by a conjecture of MaglioneVoll from group theory, we introduce and study the Poincaré-extended ab-index. This polynomial generalizes both the ab-index and the Poincaré polynomial. For posets admitting R-labelings (a relaxation of EL-labelings), we prove that the coefficients are nonnegative and give a combinatorial description of the coefficients. This proves MaglioneVoll’s conjecture as well as a conjecture of the KühneMaglione. We also define the pullback ab-index generalizing the cd-index of face posets for oriented matroids. Our results recover, generalize and unify results from BilleraEhrenborgReaddy, BergeronMykytiukSottilevan Willigenburg, SaliolaThomas, and Ehrenborg. This is joint work with Joshua Maglione and Christian Stump.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

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Meeting ID: 915 4733 5974