Unimodality shenanigans in Ehrhart theory

@misc{ferroni2026unimodality,
  title = {{Unimodality shenanigans in Ehrhart theory}},
  author = {Luis Ferroni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.10513},
  eprint = {2609.10513},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10513},
}

TY  - UNPB
TI  - Unimodality shenanigans in Ehrhart theory
AU  - Luis Ferroni
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.10513
UR  - https://arxiv.org/abs/2609.10513
AB  - We construct counterexamples to a four-decade-old conjecture attributed to Stanley concerning the unimodality of h^*-polynomials of IDP polytopes. As additional applications of our main constructions, we also disprove a conjecture by Brenti on the log-concavity of h^*-polynomials of Gorenstein IDP polytopes, and a conjecture by Ferroni and Higashitani concerning the log-concavity of the Ehrhart series of IDP polytopes. We also answer their question about the existence of very ample polytopes with non-log-concave interior Ehrhart series. Our class of examples arises by taking Cayley sums of rectangular prisms, and hence they possess regular unimodular flag triangulations by a result of Haase, Paffenholz, Piechnik and Santos. Remarkably, for the unimodality conjecture we can even find smooth counterexamples.
ER  -