Subdividing the cd-index

discrete math;combinatorics;posets;polytopes;pure math

Dornian, Patrick

University of Waterloo

关键词: discrete math;    combinatorics;    posets;    polytopes;    pure math;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/10417/3/Dornian_Patrick.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis aims to give the reader an introduction and overview of the cd-index of aposet, as well as establish some new results. We give a combinatorial proof of Ehrenborgand Karu;;s cd-index subdivision decomposition for Gorenstein* complexes and extendit to a wider class of subdivisions. In doing so, we define a local cd-index that behavesanalogously to the well studied local h-vector. We examine known cd-index and h-vectorbounds, and then use the local cd-index to bound a particular class of polytopes with thecd-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 andEhrenborg to demonstrate the structural connection between the cd-index subdivisiondecomposition and the local h-vector subdivision decomposition.