Subdividing the cd-index
Abstract
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.
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Cite this version of the work
Patrick Dornian
(2016).
Subdividing the cd-index. UWSpace.
http://hdl.handle.net/10012/10417
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