October 5, 2025Open Access

Extending the ab-index

Key Points

The Poincaré-extended ab-index is derived from the ab-index through the omega-transformation, establishing an important relationship.
This work confirms the conjecture posed by Dorpalen-Barry, Maglione, and the second author regarding posets.
The new approach provides deeper insights into ab-indices and Chow polynomials beyond R-labeled posets.
The study focuses on finite, graded, bounded posets, offering a structured perspective on their properties.

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.

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Cite This Study

Hoster et al. (Wed,) studied this question.

synapsesocial.com/papers/68e25378d6d66a53c2474324 https://doi.org/https://doi.org/10.48550/arxiv.2510.00951

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