9 citations · 27 across the 27 of their papers we have counts for
35 papers
Building monomial ideals with fixed betti numbers
Sara Faridi, Peilin Li
Motivated by the fact that as the number of generators of an ideal grows so does the complexity of calculating relations among the generators, this paper identifies collections of…
The weak Lefschetz property of whiskered graphs
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
We consider Artinian level algebras arising from the whiskering of a graph. Employing a result by Dao-Nair we show that multiplication by a general linear form has maximal rank in…
Cellular resolutions of monomial ideals and their Artinian reductions
Sara Faridi, Mohammad Farrokhi Derakhshandeh Ghouchan, Roghayyeh Ghorbani +1
The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-comp…
Simplicial Resolutions of Powers of Square-free Monomial Ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
The Taylor resolution is almost never minimal for powers of monomial ideals, even in the square-free case. In this paper we introduce a smaller resolution for each power of any squ…
Powers of graphs & applications to resolutions of powers of monomial ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers o…
Well Ordered Covers, Simplicial Bouquets, and Subadditivity of Betti Numbers of Square-Free Monomial Ideals
Sara Faridi, Mayada Shahada
Well ordered covers of square-free monomial ideals are subsets of the minimal generating set ordered in a certain way that give rise to a Lyubeznik resolution for the ideal, and ha…