We generalize the definition of the 𝑐𝑑-index of an Eulerian poset to the class of semi-Eulerian posets. For connected simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the 𝑐𝑑-index are nonnegative. This proves a conjecture of Novik for odd-dimensional manifolds and extends it to the even-dimensional case.
Juhnke, M., Samper, J.A., Venturello, L. (2026). The cd-Index of Semi-Eulerian Posets. SIAM JOURNAL ON DISCRETE MATHEMATICS, 40(2), 865-888 [10.1137/25m1723827].
The cd-Index of Semi-Eulerian Posets
Venturello, Lorenzo
2026-01-01
Abstract
We generalize the definition of the 𝑐𝑑-index of an Eulerian poset to the class of semi-Eulerian posets. For connected simplicial semi-Eulerian Buchsbaum posets, we show that all coefficients of the 𝑐𝑑-index are nonnegative. This proves a conjecture of Novik for odd-dimensional manifolds and extends it to the even-dimensional case.
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https://hdl.handle.net/11365/1320877