Extending the ab-index

Abstract

We prove for finite, graded, bounded posets, that the Poincaré-extended ab-index is obtained from the ab-index via the omega-transformation. This proves a conjecture by Dorpalen-Barry, Maglione, and the second author, and provides a more conceptual approach to ab-indices and Chow polynomials beyond R-labeled posets.

10 pages, 1 picture