English

Building reverse plane partitions with rim-hook-shaped bricks

Combinatorics 2017-01-25 v2

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.

Keywords

Cite

@article{arxiv.1612.03922,
  title  = {Building reverse plane partitions with rim-hook-shaped bricks},
  author = {Robin Sulzgruber},
  journal= {arXiv preprint arXiv:1612.03922},
  year   = {2017}
}

Comments

9 pages, (v2: typos corrected)

R2 v1 2026-06-22T17:21:30.278Z