Séminaire Lotharingien de Combinatoire, 91B.78 (2024), 10 pp.
Changxin Ding, Alex McDonough, Lilla Tóthmérész and Chi Ho Yuen
A Consistent Sandpile Torsor Algorithm for Regular Matroids
Abstract.
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 of consistency to describe classes of actions that respect deletion-contraction in a precise sense, and proved the consistency of rotor-routing torsors (and uniqueness thereof) for plane graphs.
In this work, we prove that the class of actions introduced by Backman, Baker, and the fourth author, is consistent for regular matroids.
This generalizes the above existence assertion, as well as makes progress on the goal of classifying all consistent actions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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