8 papers · 1 filter
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…
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…
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…
Splittings of Ideals of Points in
Elena Guardo, Graham Keiper, Adam Van Tuyl
Let be the bihomogeneous ideal of a finite set of points . The purpose of this note is to consider ``splitting…
The -vectors of toric ideals of odd cycle compositions revisited
Kieran Bhaskara, Adam Van Tuyl, Sasha Zotine
Let be a graph consisting of odd cycles that all share a common vertex. Bhaskara, Higashitani, and Shibu Deepthi recently computed the -polynomial for the quotient ring…