Lecture Hall Partitions and the Affine Hyperoctahedral Group

Christopher R. H. Hanusa; Carla D. Savage

doi:10.37236/7201

Christopher R. H. Hanusa
Carla D. Savage

Keywords: Hyperoctahedral group, Lecture hall partition, s-Lecture hall partition, Signed permutation, Truncated lecture hall partition, Inversions, Descent set, Quadratic statistic, Coxeter group, Type C, Bott's formula, inv, amaj, lhp, comaj

Abstract

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 $\widetilde{C}/C$.