The $cd$-index of semi-Eulerian posets

TL;DR

This paper extends the $cd$-index concept from Eulerian to semi-Eulerian posets and proves non-negativity of coefficients for certain Buchsbaum posets, confirming a conjecture for manifolds of all dimensions.

Contribution

It generalizes the $cd$-index to semi-Eulerian posets and proves non-negativity for Buchsbaum cases, extending Novik's conjecture to all dimensions.

Findings

Coefficients of the $cd$-index are non-negative for simplicial semi-Eulerian Buchsbaum posets.

The non-negativity result confirms Novik's conjecture for odd-dimensional manifolds.

Extension of the $cd$-index to semi-Eulerian posets broadens its applicability.

Abstract

We generalize the definition of the $cd$-index of an Eulerian poset to the class of semi-Eulerian posets. For simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the $cd$-index are non-negative. This proves a conjecture of Novik for odd dimensional manifolds and extends it to the even dimensional case.