The expansion of half-integral polytopes
<|reference_start|>The expansion of half-integral polytopes: The expansion of a polytope is an important parameter for the analysis of the random walks on its graph. A conjecture of Mihai and Vazirani states that all $0/1$-polytopes have expansion at least 1. We show that the generalization to half-integral polytopes does not hold by constructing $d$-dimensional half-integral polytopes whose expansion decreases exponentially fast with $d$. We also prove that the expansion of half-integral zonotopes is uniformly bounded away from $0$. As an intermediate result, we show that half-integral zonotopes are always graphical.<|reference_end|>
@article{cardinal2024the,
    title={The expansion of half-integral polytopes},
    author={Jean Cardinal, Lionel Pournin},
    journal={arXiv preprint arXiv:2402.14343},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.14343},
    primaryClass={math.CO cs.CG cs.DM math.MG}
}