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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∗-polynomial is real-rooted thereby complementing previous results of Savage-Visontai and Brändén-Leander.

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Cite

BibTeXRIS
BibTeX
@misc{jochemko2026weighted,
  title = {{Weighted lattice point enumeration in lecture hall order polytopes}},
  author = {Katharina Jochemko and Krishna Menon},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17250},
  eprint = {2609.17250},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17250},
}
RIS
TY  - UNPB
TI  - Weighted lattice point enumeration in lecture hall order polytopes
AU  - Katharina Jochemko
AU  - Krishna Menon
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17250
UR  - https://arxiv.org/abs/2609.17250
AB  - 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^∗-polynomial is real-rooted thereby complementing previous results of Savage-Visontai and Brändén-Leander.
ER  -