6 citations · 12 across the 11 of their papers we have counts for
11 papers
Chip-Firing and the Sandpile Group of the Matroid
Michael Ion, Alex McDonough
A celebrated result of Seymour is that all regular matroids are built up from graphic matroids, cographic matroids, and a specific 10 element rank 5 matroid called . In thi…
A Consistent Sandpile Torsor Algorithm for Regular Matroids
Changxin Ding, Alex McDonough, Lilla Tóthmérész +1
Every regular matroid is associated with a sandpile group, which acts simply transitively on the set of bases in various ways. Ganguly and the second author introduced the notion o…
Fragmenting any Parallelepiped into a Signed Tiling
Joseph Doolittle, Alex McDonough
It is broadly known that any parallelepiped tiles space by translating copies of itself along its edges. In earlier work relating to higher-dimensional sandpile groups, the second…
Torsors and tilings from toric toggling
Colin Defant, Michael Joseph, Matthew Macauley +1
Much of dynamical algebraic combinatorics focuses on global dynamical systems defined via maps that are compositions of local toggle operators. The second author and Roby studied s…
Sampling planar tanglegrams and pairs of disjoint triangulations
Alexander E. Black, Kevin Liu, Alex Mcdonough +4
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that th…
Realizable Standard Young Tableaux
Igor Araujo, Alexander E. Black, Amanda Burcroff +3
Given two vectors and , their outer sum is given by the matrix with entries . If the entries of and are increasing and sufficiently gener…
Rotor-Routing Induces the Only Consistent Sandpile Torsor Structure on Plane Graphs
Ankan Ganguly, Alex McDonough
We make precise and prove a conjecture of Klivans about actions of the sandpile group on spanning trees. More specifically, the conjecture states that there exists a unique ``suita…
A family of matrix-tree multijections
Alex McDonough
For a natural class of integer matrices, we construct a non-convex polytope which periodically tiles . From this tiling, we provide a family of geometrica…
Matching complexes of trees and applications of the matching tree algorithm
Marija Jelić Milutinović, Helen Jenne, Alex McDonough +1
A matching complex of a simple graph is a simplicial complex with faces given by the matchings of . The topology of matching complexes is mysterious; there are few graphs fo…
Determining Genus From Sandpile Torsor Algorithms
Alex McDonough
We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha].…
Combinatorial and Asymptotical Results on the Neighborhood Grid
Martin Skrodzki, Ulrich Reitebuch, Alex McDonough
In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental…