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Subdividing the cd-index

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Dornian_Patrick.pdf (464.02 KB)

Date

2016-04-28

Authors

Dornian, Patrick

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University of Waterloo

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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Keywords

discrete math, combinatorics, posets, polytopes, pure math

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URI

http://hdl.handle.net/10012/10417

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Theses
Combinatorics and Optimization