Séminaire Lotharingien de Combinatoire, 78B.65 (2017), 12 pp.
Building Reverse Plane Partitions with Rim-Hook-Shaped Bricks
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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