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arXiv · 1708.09720

Greene--Kleitman invariants for Sulzgruber insertion

Alexander Garver·Rebecca Patrias
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Abstract

R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that Hillman-Grassl may be equivalently defined using the Robinson-Schensted-Knuth correspondence, and we show the analogous result for Sulzgruber's insertion. We refer to our description of Sulzgruber's insertion as diagonal RSK. As a consequence of this equivalence, we show that Sulzgruber's map from multisets of rim hooks to reverse plane partitions can be expressed in terms of Greene-Kleitman invariants.

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Alexander Garver, Rebecca Patrias. 2017-08-31. Greene--Kleitman invariants for Sulzgruber insertion. https://arxiv.org/abs/1708.09720

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