Séminaire Lotharingien de Combinatoire, 78B.65 (2017), 12 pp.

Robin Sulzgruber

Building Reverse Plane Partitions with Rim-Hook-Shaped Bricks

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.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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