Inserting rim-hooks into reverse plane partitions
Combinatorics
2018-05-22 v2
Abstract
A new algorithm for inserting rim-hooks into reverse plane partitions is presented. The insertion is used to define a bijection between reverse plane partitions of a fixed shape and multi-sets of rim-hooks. In turn this yields a bijective proof of the fact that the generating function for reverse plane partitions of a fixed shape, which was first obtained by R. Stanley, factors into a product featuring the hook-lengths of this shape. Our bijection turns out to be equivalent to a map defined by I. Pak by different means, and can be related to the Hillman-Grassl correspondence and the Robinson-Schensted-Knuth correspondence.
Cite
@article{arxiv.1710.09695,
title = {Inserting rim-hooks into reverse plane partitions},
author = {Robin Sulzgruber},
journal= {arXiv preprint arXiv:1710.09695},
year = {2018}
}
Comments
v2: 20 pages, 19 figures, minor changes and corrections (v1: 19 pages, 19 figures)