Given a family of lattice polytopes, a common endeavor in Ehrhart theory is the classification of those polytopes in the family that are Gorenstein, or more generally level. In this article, we consider these questions for ${\boldsymbol s}$-lecture hall polytopes, which are a family of simplices arising from $\mathbf {s}$-lecture hall partitions. In particular, we provide concrete classifications for both of these properties purely in terms of ${\boldsymbol s}$-inversion sequences. Moreover, for a large subfamily of ${\boldsymbol s}$-lecture hall polytopes, we provide a more geometric classification of the Gorenstein property in terms of its tangent cones. We then show how one can use the classification of level ${\boldsymbol s}$-lecture hall polytopes to construct infinite families of level ${\boldsymbol s}$-lecture hall polytopes, and to describe level ${\boldsymbol s}$-lecture hall polytopes in small dimensions.
@article{10_37236_8626,
author = {Florian Kohl and McCabe Olsen},
title = {Level algebras and \(\boldsymbol{s}\)-lecture hall polytopes},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {3},
doi = {10.37236/8626},
zbl = {1448.51013},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8626/}
}
TY - JOUR
AU - Florian Kohl
AU - McCabe Olsen
TI - Level algebras and \(\boldsymbol{s}\)-lecture hall polytopes
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8626/
DO - 10.37236/8626
ID - 10_37236_8626
ER -
%0 Journal Article
%A Florian Kohl
%A McCabe Olsen
%T Level algebras and \(\boldsymbol{s}\)-lecture hall polytopes
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8626/
%R 10.37236/8626
%F 10_37236_8626
Florian Kohl; McCabe Olsen. Level algebras and \(\boldsymbol{s}\)-lecture hall polytopes. The electronic journal of combinatorics, Tome 27 (2020) no. 3. doi: 10.37236/8626
