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arXiv · 2609.17250

Weighted lattice point enumeration in lecture hall order polytopes

Katharina Jochemko·Krishna Menon
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Abstract

We consider weighted lattice point enumeration in lecture hall order polytopes. We observe that these half-open polytopes are closed under weight-lifting for a large class of polynomial weights, including monomials and weights given by binomial coefficients. For rooted trees, we prove that the corresponding (weighted) $h^\ast$-polynomial is real-rooted thereby complementing previous results of Savage-Visontai and Brändén-Leander.

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Katharina Jochemko, Krishna Menon. 2026-09-15. Weighted lattice point enumeration in lecture hall order polytopes. https://arxiv.org/abs/2609.17250

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