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Some estimates for the number of vertices of integer polyhedra

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Abstract

A polyhedron is called integer if its every vertex has integer coordinates. We consider integer polyhedra P I = conv(P ∩ ℤd) defined implicitly; that is, no system of linear inequalities is known for P I but some is known for P. Some estimates are given for the number of vertices of P I .

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, State University of Nizhnii Novgorod, pr. Gagarina 23, Nizhnii Novgorod, 603950, Russia

    S. I. Veselov & A. Yu. Chirkov

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  1. S. I. Veselov
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  2. A. Yu. Chirkov
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Correspondence to S. I. Veselov.

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Original Russian Text © S.I. Veselov, A.Yu. Chirkov, 2007, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 2, 2007, Vol. 14, No. 2, pp. 14–31.

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Veselov, S.I., Chirkov, A.Y. Some estimates for the number of vertices of integer polyhedra. J. Appl. Ind. Math. 2, 591–604 (2008). https://doi.org/10.1134/S1990478908040157

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