The $cd$-index of semi-Eulerian posets

Jos\'e Alejandro Samper; Lorenzo Venturello; Martina Juhnke-Kubitzke

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The $cd$-index of semi-Eulerian posets

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arxiv 2405.05812 v1 pith:OBG7GWVV submitted 2024-05-09 math.CO

Martina Juhnke-Kubitzke , José Alejandro Samper , Lorenzo Venturello This is my paper

classification math.CO

keywords indexposetssemi-euleriandimensionalbuchsbaumcaseclasscoefficients

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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.

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