A simple explanation for the “shuffling phenomenon” for lozenge tilings of dented hexagons

Abstract

In a recent preprint, Lai and Rohatgi proved a “shuffling theorem” for lozenge tilings of a hexagon with “dents” (i.e., missing triangles). Here, we shall point out that this follows immediately from the enumeration of Gelfand–Tsetlin patterns with given bottom row. This observation is also contained in a recent preprint of Byun.