6 citations · 9 across the 4 of their papers we have counts for
7 papers
Projective dimension of Hypergraphs
Kuei-Nuan Lin, Sonja Mapes
Given a square-free monomial ideal , satisfying certain hypotheses, in a polynomial ring over a field , we compute the projective dimension of . Specifically,…
Lattices and Hypergraphs associated to square-free monomial ideals
Kuei-Nuan Lin, Sonja Mapes
Given a square-free monomial ideal in a polynomial ring over a field , one can associate it with its LCM-lattice and its hypergraph. In this short note, we esta…
Constructing monomial ideals with a given minimal resolution
Sonja Mapes, Lindsay C. Piechnik
This paper gives a description of various recent results which construct monomial ideals with a given minimal free resolution. We show that these are all instances of coordinatizin…
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…
Partially ordered sets in Macaulay2
David Cook, Sonja Mapes, Gwyneth Whieldon
We introduce the package Posets for Macaulay2. This package provides a data structure and the necessary methods for working with partially ordered sets, also called posets. In part…
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…
Finite atomic lattices and resolutions of monomial ideals
Sonja Mapes
In this paper we primarily study monomial ideals and their minimal free resolutions by studying their associated LCM lattices. In particular, we formally define the notion of coord…