In 1997 Bousquet-Mélou and Eriksson introduced lecture hall partitions as the inversion vectors of elements of the parabolic quotient $\widetilde{C}/C$. We provide a new view of their correspondence that allows results in one domain to be translated into the other. We determine the equivalence between combinatorial statistics in each domain and use this correspondence to translate certain generating function formulas on lecture hall partitions to new observations about $\widetilde{C}/C$.
@article{10_37236_7201,
author = {Christopher R. H. Hanusa and Carla D. Savage},
title = {Lecture {Hall} partitions and the affine hyperoctahedral group},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/7201},
zbl = {1380.05009},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7201/}
}
TY - JOUR
AU - Christopher R. H. Hanusa
AU - Carla D. Savage
TI - Lecture Hall partitions and the affine hyperoctahedral group
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/7201/
DO - 10.37236/7201
ID - 10_37236_7201
ER -
%0 Journal Article
%A Christopher R. H. Hanusa
%A Carla D. Savage
%T Lecture Hall partitions and the affine hyperoctahedral group
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/7201/
%R 10.37236/7201
%F 10_37236_7201
Christopher R. H. Hanusa; Carla D. Savage. Lecture Hall partitions and the affine hyperoctahedral group. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7201
