9 citations · 15 across the 6 of their papers we have counts for
7 papers
Minimal free resolutions of monomial ideals and of toric rings are supported on posets
Timothy B. P. Clark, Alexandre B. Tchernev
We introduce the notion of a \emph{resolution supported on a poset}. When the poset is a CW-poset, i.e. the face poset of a regular CW-complex, we recover the notion of cellular re…
Moments of the inverse participation ratio for the Laplacian on finite regular graphs
Timothy B. P. Clark, Adrian Del Maestro
We investigate the first and second moments of the inverse participation ratio (IPR) for all eigenvectors of the Laplacian on finite random regular graphs with vertices and deg…
The Betti poset in monomial resolutions
Timothy B. P. Clark, Sonja Mapes
Let be a finite partially ordered set with unique minimal element . We study the Betti poset of , created by deleting elements for which the open interval…
Regular CW-complexes and poset resolutions of monomial ideals
Timothy B. P. Clark, Alexandre Tchernev
We use the natural homeomorphism between a regular CW-complex X and its face poset P_X to establish a canonical isomorphism between the cellular chain complex of X and the result o…
Rigid monomial ideals
Timothy B. P. Clark, Sonja Mapes
In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we sho…
A Minimal Poset Resolution of Stable Ideals
Timothy B. P. Clark
We use the theory of poset resolutions to construct the minimal free resolution of an arbitrary stable monomial ideal in the polynomial ring whose coefficients are from a field. Th…
Poset Resolutions of Monomial Ideals
Timothy B. P. Clark
We introduce the class of lattice-linear monomial ideals and use the LCM-lattice to give an explicit construction for their minimal free resolution. The class of lattice-linear ide…