Hilbert Bases and Lecture Hall Partitions

Abstract

In the interest of finding the minimum additive generating set for the set of $\mathbf{s}$-lecture hall partitions, we compute the Hilbert bases for the $\mathbf{s}$-lecture hall cones in certain cases. In particular, we compute the Hilbert bases for two well-studied families of sequences, namely the $1\mathrm{mod}k$ sequences and the $\ell$-sequences. Additionally, we provide a characterization of the Hilbert bases for $\mathbf{u}$-generated Gorenstein $\mathbf{s}$-lecture hall cones in low dimensions.

arXiv commentFinal Version. To appear in Ramanujan J