3 papers
math.AC2026
Constructing Koszul filtrations: existence and non-existence for G-quadratic algebras
Emily Berghofer, Lisa Nicklasson, Peder Thompson +1
Given a standard graded algebra over a field, we consider the relationship between G-quadraticity and the existence of a Koszul filtration. We show that having a quadratic Gröbner…
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…
math.AC2025
Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
Thiago Holleben, Lisa Nicklasson
Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of artinian Gorenstein algebras with unconstrained Hilbert series, which we call Roller Coaster alg…