Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifting properties of maximal lattice-free polyhedra   We study the uniqueness of minimal liftings of cut-generating functions
obtained from maximal lattice-free polyhedra. We prove a basic invariance
property of unique minimal liftings for general maximal lattice-free polyhedra.
This generalizes a previous result by Basu, Cornu\'ejols and K\"oppe~\cite{bcm}
for {\em simplicial} maximal lattice-free polytopes, thus completely settling
this fundamental question about lifting for maximal lattice-free polyhedra. We
further give a very general iterative construction to get maximal lattice-free
polyhedra with the unique-lifting property in arbitrary dimensions. This single
construction not only obtains all previously known polyhedra with the
unique-lifting property, but goes further and vastly expands the known list of
such polyhedra. Finally, we extend characterizations from~\cite{bcm} about
lifting with respect to maximal lattice-free simplices to more general
polytopes. These nontrivial generalizations rely on a number of results from
discrete geometry, including the Venkov-Alexandrov-McMullen theorem on
translative tilings and characterizations of zonotopes in terms of central
symmetry of their faces.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg