R. Sulzgruber's rim hook insertion and the Hillman–Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets of rim-hooks of the same partition shape. It is known that Hillman–Grassl may be equivalently defined using the Robinson–Schensted–Knuth correspondence, and we show the analogous result for Sulzgruber's insertion. We refer to our description of Sulzgruber's insertion as diagonal RSK. As a consequence of this equivalence, we show that Sulzgruber's map from multisets of rim hooks to reverse plane partitions can be expressed in terms of Greene–Kleitman invariants.
@article{10_37236_7992,
author = {Alexander Garver and Rebecca Patrias},
title = {Greene-Kleitman invariants for {Sulzgruber} insertion},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/7992},
zbl = {1417.05014},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7992/}
}
TY - JOUR
AU - Alexander Garver
AU - Rebecca Patrias
TI - Greene-Kleitman invariants for Sulzgruber insertion
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/7992/
DO - 10.37236/7992
ID - 10_37236_7992
ER -
%0 Journal Article
%A Alexander Garver
%A Rebecca Patrias
%T Greene-Kleitman invariants for Sulzgruber insertion
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7992/
%R 10.37236/7992
%F 10_37236_7992
Alexander Garver; Rebecca Patrias. Greene-Kleitman invariants for Sulzgruber insertion. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/7992
