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4 papers
Non-Eulerian Dehn-Sommerville relations
Connor Sawaske, Lei Xue
The classical Dehn--Sommerville relations assert that the -vector of an Eulerian simplicial complex is symmetric. We establish three generalizations of the Dehn--Sommerville rel…
Algebraic -vectors of simplicial complexes through local cohomology, part 1
Connor Sawaske
Given an infinite field and a simplicial complex , a common theme in studying the - and -vectors of has been the consideration of the Hilbert series of th…
Ext and local cohomology modules of face rings of simplicial posets
Connor Sawaske
There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results…
Almost Buchsbaumness of some rings arising from complexes with isolated singularities
Connor Sawaske
We study properties of the Stanley-Reisner rings of simplicial complexes with isolated singularities modulo two generic linear forms. Miller, Novik, and Swartz proved that if a com…