2016/12/12 by Robin Sulzgruber, Sulzgruber, Robin
Mathematics · Physics and Astronomy · #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1612.03922
openalex publication_date 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.