11 papers
Geometrically vertex decomposable star configurations
Susan M. Cooper, Emanuela Marangone, Elena Guardo +1
The goal of this paper is to determine how the family of ideals of star configurations intersects with the class of geometrically vertex decomposable ideals. The main result of thi…
Trivariate Splines on Fans of Hyperplane Arrangements and Koszul Homology
Carles Checa, Michael DiPasquale, Pablo Mazón +5
We study the space of splines where denotes a smoothness distribution and is the fan of a central hyperpl…
The van der Waerden Simplicial Complex and its Lefschetz Properties
Naveena Ragunathan, Adam Van Tuyl
The van der Waerden simplicial complex, denoted , is the simpicial complex whose facets correspond to the arithmetic progressions of length in the set $\{1,\ldo…
Geometric vertex decomposition and liaison for toric ideals of graphs
Mike Cummings, Sergio Da Silva, Jenna Rajchgot +1
The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic generalization of the vertex decomposability property for simplicial complexes. Indeed, a…
Levelable graphs
Kieran Bhaskara, Michael Y. C. Chong, Takayuki Hibi +2
We study a family of positive weighted well-covered graphs, which we call levelable graphs, that are related to a construction of level artinian rings in commutative algebra. A gra…
Analytic spread of binomial edge ideals
Eduardo Camps-Moreno, Deblina Dey, Souvik Dey +5
We investigate the analytic spread of binomial edge ideals of finite simple graphs. We provide tight bounds for this invariant in general. For special families of graphs (e.g., clo…