3 citations · 3 across the 4 of their papers we have counts for
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Optimal Betti numbers of forest ideals
Michael Goff
We prove a tight lower bound on the Betti numbers of tree and forest ideals and a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.
Bounding Betti numbers of bipartite graph ideals
Michael Goff
We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs.
On the multiplicity conjecture for non-Cohen-Macaulay simplicial complexes
Michael Goff
We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with ma…
Bounding Multiplicity by Shifts in the Taylor Resolution
Michael Goff
A weaker form of the multiplicity conjecture of Herzog, Huneke, and Srinivasan is proven for two classes of monomial ideals: quadratic monomial ideals and squarefree monomial ideal…