Building reverse plane partitions with rim-hook-shaped bricks

Robin Sulzgruber

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arXiv · 1612.03922

Building reverse plane partitions with rim-hook-shaped bricks

Robin Sulzgruber

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Abstract

The generating function of reverse plane partitions of a fixed shape factors into a product featuring the hook-lengths of this shape. This result, which was first obtained by Stanley, can be explained bijectively using the Hillman-Grassl correspondence between reverse plane partitions and tableaux weighted by hook-lengths. In this extended abstract an alternative bijection between the same families of objects is presented. This construction is best perceived as a set of rules for building reverse plane partitions, viewed as arrangements of stacks of cubes, using bricks in the shape of rim-hooks.

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Robin Sulzgruber. 2016-12-12. Building reverse plane partitions with rim-hook-shaped bricks. https://arxiv.org/abs/1612.03922

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