7 papers
Line Shellings of Geometric Lattices
Spencer Backman, Galen Dorpalen-Barry, Anastasia Nathanson +2
Inspired by Bruggesser-Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid…
Cleanliness and the Varchenko-Gelfand algebra
Graham Denham, Galen Dorpalen-Barry, Nicholas Proudfoot
A central question in the theory of hyperplane arrangements is when the complement of a complex arrangement is aspherical. Barkley and Speyer introduced a class of real arrangement…
Salvetti complexes for conditional oriented matroids
Galen Dorpalen-Barry, Dan Dugger, Nicholas Proudfoot
We give a new proof of the fact that the complement of the complexification of a real hyperplane arrangement is homotopy equivalent to the Salvetti complex of the associated orient…
The Ehrhart polynomial of a matroid specializes to the beta invariant
Anastasia Chavez, Galen Dorpalen-Barry, Luis Ferroni +3
We show that the linear coefficient of the Ehrhart polynomial of a matroid base polytope evaluated at is equal to, up to normalization, the -invariant of the matroid. This…
The geometry of zonotopal algebras I: cohomology of graphical configuration spaces
Colin Crowley, Galen Dorpalen-Barry, André Henriques +1
Zonotopal algebras of vector arrangements are combinatorially-defined algebras with connections to approximation theory, introduced by Holtz and Ron and independently by Ardila and…
Enumerating Parking Completions Using Join and Split
Ayomikun Adeniran, Steve Butler, Galen Dorpalen-Barry +5
Given a strictly increasing sequence with entries from , a parking completion is a sequence with and $|…