5 citations · 9 across the 13 of their papers we have counts for
14 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…
A Three-Regime Theorem for Flow-Firing
Sarah Brauner, Galen Dorpalen-Barry, Selvi Kara +2
Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize c…
The Poincaré-extended ab-index
Galen Dorpalen-Barry, Joshua Maglione, Christian Stump
Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré-extended ab-index, which gen…
Equivariant cohomology and conditional oriented matroids
Galen Dorpalen-Barry, Nicholas Proudfoot, Jidong Wang
We give a cohomological interpretation of the Heaviside filtration on the Varchenko--Gelfand ring of a pair , where is a real hyperplane ar…
Shi arrangements restricted to Weyl cones
Galen Dorpalen-Barry, Christian Stump
We consider the restrictions of Shi arrangements to Weyl cones, their relations to antichains in the root poset, and their intersection posets. For any Weyl cone, we provide biject…
The Varchenko-Gel'fand Ring of a Cone
Galen Dorpalen-Barry
For a hyperplane arrangement in a real vector space, the coefficients of its Poincaré polynomial have many interpretations. An interesting one is provided by the Varchenko-Gel'fand…
Filtering cohomology of ordinary and Lagrangian Grassmannians
The 2020 Polymath Jr. REU "q-binomials, the Grassmannian group", : +31
This paper studies, for a positive integer , the subalgebra of the cohomology ring of the complex Grassmannians generated by the elements of degree at most . We build in two…
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 $|…
Whitney Numbers for Poset Cones
Galen Dorpalen-Barry, Jang Soo Kim, Victor Reiner
Hyperplane arrangements dissect into connected components called chambers, and a well-known theorem of Zaslavsky counts chambers as a sum of nonnegative integers cal…
A positivity phenomenon in Elser's Gaussian-cluster percolation model
Galen Dorpalen-Barry, Cyrus Hettle, David C. Livingston +4
Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideratio…