Abstract
We study a family of lattice polytopes, called primitive zonotopes, describe instances with small parameters, and discuss connections to the largest diameter of lattice polytopes and to the computational complexity of multicriteria matroid optimization. Complexity results and open questions are also presented.
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Acknowledgements
The authors thank the anonymous referees, Johanne Cohen, Nathann Cohen, Komei Fukuda, and Aladin Virmaux for valuable comments and for informing us of reference [31], Emo Welzl and Günter Ziegler for helping us access Thorsten Thiele’s Diplomarbeit, Dmitrii Pasechnik for pointing out reference [29], and Vincent Pilaud for pointing out that \(Z_1(d,2)\) is the permutahedron of type \(B_d\). This work was partially supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant program (RGPIN-2015-06163), by the Digiteo Chair C&O program at Université de Paris Sud, and by the Dresner Chair at the Technion.
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Deza, A., Manoussakis, G., Onn, S. (2018). Small Primitive Zonotopes. In: Conder, M., Deza, A., Weiss, A. (eds) Discrete Geometry and Symmetry. GSC 2015. Springer Proceedings in Mathematics & Statistics, vol 234. Springer, Cham. https://doi.org/10.1007/978-3-319-78434-2_5
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