Evacuation of Rectangular Standard Young Tableaux and Chip-firing

We elaborate upon a bijection discovered by Cools et al. in [CDPR10] between, on the one hand, rectangular standard Young tableaux, and, on the other hand, representatives, known as G-parking functions, of chip configurations on certain graphs modulo the chip-firing equivalence relation. We present an explcit formula for computing the G-parking function associated to a given tableau, and prove that evacuation on tableaux corresponds (under the bijection) to a vertical reflection on the graph.