Balanced vertex decomposable simplicial complexes and their h-vectors
Presenter
February 15, 2013
Abstract
Given any finite simplicial complex Delta, we will discuss how to construct a simplicial complex Delta_chi that is balanced and vertex decomposable. This new simplicial complex has the property that its h-vector is precisely the f-vector of the original complex Delta. This construction generalizes the "whiskering" construction of Villareal, and Cook and Nagel. As an application, we will show how to use this construction to construct a square-free monomial ideal with a particular sequence of Betti numbers obtained from the f-vector of a simplicial complex.