Subdividing the cd-index
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This thesis aims to give the reader an introduction and overview of the cd-index of a poset, as well as establish some new results. We give a combinatorial proof of Ehrenborg and Karu's cd-index subdivision decomposition for Gorenstein* complexes and extend it to a wider class of subdivisions. In doing so, we define a local cd-index that behaves analogously to the well studied local h-vector. We examine known cd-index and h-vector bounds, and then use the local cd-index to bound a particular class of polytopes with the cd-index of a stacked polytope. We conclude by investigating the h-vector and local h- vector of posets in full generality, and use an algebra morphism developed by Bayer and Ehrenborg to demonstrate the structural connection between the cd-index subdivision decomposition and the local h-vector subdivision decomposition.
Cite this version of the work
Patrick Dornian (2016). Subdividing the cd-index. UWSpace. http://hdl.handle.net/10012/10417