A. McDonough

activity

20242026

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math.CO2026

Realizable Standard Young Tableaux

Igor Araujo, Alexander E. Black, Amanda Burcroff +3

Given two vectors $u$ and $v$ , their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$ . If the entries of $u$ and $v$ are increasing and sufficiently gener…

math.CO2025

Chip-Firing and the Sandpile Group of the $R_{10}$ 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 $R_{10}$ . In thi…

math.CO2025

A Consistent Sandpile Torsor Algorithm for Regular Matroids

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…

math.CO2024

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…

Realizable Standard Young Tableaux

Chip-Firing and the Sandpile Group of the R10​ Matroid

A Consistent Sandpile Torsor Algorithm for Regular Matroids

Fragmenting any Parallelepiped into a Signed Tiling

Chip-Firing and the Sandpile Group of the $R_{10}$ Matroid