16 citations · 71 across the 20 of their papers we have counts for
20 papers
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…
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…
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…
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…
On binomial complete intersections
Filip Jonsson Kling, Samuel Lundqvist, Lisa Nicklasson
We consider homogeneous binomial ideals in , where and . When such an ideal is a complete inte…
Chain algebras of finite distributive lattices
Oleksandra Gasanova, Lisa Nicklasson
We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes we conclude that every such algebra is…
Hilbert functions and Jordan type of Perazzo Artinian algebras
Nancy Abdallah, Nasrin Altafi, Pietro De Poi +6
We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Pe…
Monomial projections of Veronese varieties: new results and conjectures
Liena Colarte-Gómez, Rosa M. Miró-Roig, Lisa Nicklasson
In this paper, we consider the homogeneous coordinate rings of monomial projections of Veronese varieties parameterized by subsets…
Toric and non-toric Bayesian networks
Lisa Nicklasson
In this paper we study Bayesian networks from a commutative algebra perspective. We characterize a class of toric Bayesian nets, and provide the first example of a Bayesian net whi…
Syzygies, constant rank, and beyond
Marc Härkönen, Lisa Nicklasson, Bogdan Raiţă
We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compact…
Staged tree models with toric structure
Christiane Görgen, Aida Maraj, Lisa Nicklasson
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric…
Products of polymatroids with the strong exchange property
Lisa Nicklasson
It was conjectured by White in 1980 that the toric ring associated to a matroid is defined by symmetric exchange relations. This conjecture was extended to discrete polymatroids by…
Gorenstein rings generated by strongly stable sets of quadratic monomials
Ralf Fröberg, Lisa Nicklasson
We characterize all Gorenstein rings generated by strongly stable sets of monomials of degree two. We compute their Hilbert series in several cases, which also provides an answer t…
On decomposing monomial algebras with the Lefschetz properties
Oleksandra Gasanova, Samuel Lundqvist, Lisa Nicklasson
We introduce a general technique for decomposing monomial algebras which we use to study the Lefschetz properties. We apply our technique to various classes of algebras, including…
Subalgebras generated in degree two with minimal Hilbert function
Lisa Nicklasson
What can be said about the subalgebras of the polynomial ring, with minimal or maximal Hilbert function? This question was discussed in a recent paper by M. Boij and A. Conca. In t…
On the Betti numbers and Rees algebras of ideals with linear powers
Lisa Nicklasson
An ideal is said to have linear powers if has a linear minimal free resolution, for all . In this paper we study the Betti numbers…
On generic principal ideals in the exterior algebra
Samuel Lundqvist, Lisa Nicklasson
We give a lower bound on the Hilbert series of the exterior algebra modulo a principal ideal generated by a generic form of odd degree and disprove a conjecture by Moreno-Socías an…
The strong Lefschetz property of monomial complete intersections in two variables
Lisa Nicklasson
In this paper we classify the monomial complete intersection algebras, in two variables, and of positive characteristic, which has the strong Lef- schetz property. Together with kn…
On the structure of monomial complete intersections in positive characteristic
Samuel Lundqvist, Lisa Nicklasson
In this paper we study the Lefschetz properties of monomial complete intersections in positive characteristic. We give a complete classification of the strong Lefschetz property wh…
On the Hilbert series of ideals generated by generic forms
Lisa Nicklasson
There is a longstanding conjecture by Fröberg about the Hilbert series of the ring , where is a polynomial ring, and an ideal generated by generic forms. We prove this…