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R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence aretwo distinct bijections between the reverse plane partitions of a fixedpartition shape and multisets of rim-hooks of the same partition shape. It isknown that Hillman-Grassl may be equivalently defined using theRobinson-Schensted-Knuth correspondence, and we show the analogous result forSulzgruber's insertion. We refer to our description of Sulzgruber's insertionas diagonal RSK. As a consequence of this equivalence, we show thatSulzgruber's map from multisets of rim hooks to reverse plane partitions can beexpressed in terms of Greene-Kleitman invariants.

Greene--Kleitman invariants for Sulzgruber insertion