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arXiv · 1703.02006

Hilbert Bases and Lecture Hall Partitions

McCabe Olsen
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Abstract

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

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McCabe Olsen. 2017-06-16. Hilbert Bases and Lecture Hall Partitions. https://arxiv.org/abs/1703.02006

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