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math.AC2025
Divisibility Relations and -Extremal ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other gen…
math.AC2025
Simplicial Resolutions of the Quadratic Power of Monomial Ideals
Susan M. Cooper, Sara Faridi, Hasan Mahmood
Given any monomial ideal minimally generated by monomials, we define a simplicial complex that supports a resolution of . We also define a subco…
math.CO2025
Spheres and balls as independence complexes
Susan M. Cooper, Sara Faridi, Thiago Holleben +2
The terms "whiskering", and more generally "grafting", refer to adding generators to any monomial ideal to make the resulting ideal Cohen-Macaulay. We investigate the independence…