naa a22 4500 510736718 CHVBK 20180411083012.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-012-0092-8 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0092-8 Averkov Gennadiy University of Magdeburg, 39106, Magdeburg, Germany aut A proof of Lovász's theorem on maximal lattice-free sets [Elektronische Daten] [Gennadiy Averkov] Let K be a maximal lattice-free set in $${\mathbb{R}^d}$$ , that is, K is convex and closed subset of $${\mathbb{R}^d}$$ , the interior of K does not contain points of $${\mathbb{Z}^d}$$ and K is inclusion-maximal with respect to the above properties. A result of Lovász asserts that if K is d-dimensional, then K is a polyhedron with at most 2 d facets, and the recession cone of K is a linear space spanned by vectors from $${\mathbb{Z}^d}$$ . A first complete proof of mentioned Lovász's result has been published in a paper of Basu, Conforti, Cornuéjols and Zambelli (where the authors use Dirichlet's approximation as a tool). The aim of this note is to give another proof of this result. Our proof relies on Minkowki's first fundamental theorem from the geometry of numbers. We remark that the result of Lovász is relevant in integer and mixed-integer optimization. The Managing Editors, 2012 Cutting plane nationallicence Lattice-free set nationallicence Lovász's theorem nationallicence Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 105-109 0138-4821 54:1<105 2013 54 13366 https://doi.org/10.1007/s13366-012-0092-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0092-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Averkov Gennadiy University of Magdeburg, 39106, Magdeburg, Germany aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 105-109 0138-4821 54:1<105 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer