Abstract Convergent rewriting systems on algebraic structures give methods to solve decision problems, prove coherence results, and compute homological invariants. These are based higher-dimensional extensions of the critical branching lemma that proves local confluence from branchings. The analysis structures, such as groups or linear algebras, is complicated because underlying axioms. This ar...

In 2016, Hopkins, McConville, and Propp proved that labeled chip-firing on a line always leaves the chips in sorted order provided initial number of is even. We present novel proof this result. then apply our methods to resolve related conjectures concerning confluence systems.

Siu L. Chow Department of Psychology, University of Regina, Canada