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arXiv · 1710.09695

Inserting rim-hooks into reverse plane partitions

Robin Sulzgruber
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Abstract

A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective proof of the fact that the generating function for reverse plane partitions of a fixed shape, which was first obtained by R. Stanley, factors into a product featuring the hook-lengths of this shape. Our bijection turns out to be equivalent to a map defined by I. Pak by different means, and can be related to the Hillman-Grassl correspondence and the Robinson-Schensted-Knuth correspondence.

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Robin Sulzgruber. 2017-10-26. Inserting rim-hooks into reverse plane partitions. https://arxiv.org/abs/1710.09695

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