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- W2952172692 abstract "A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of $R^n$. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these ``partial quotients'', so called determinants, are defined. It is proved that the facets of all the $2^n$ Klein polyhedra generated by a lattice $La$ have uniformly bounded determinants if and only if the facets and the edge stars of the vertices of the Klein polyhedron generated by $La$ and related to the positive orthant have uniformly bounded determinants." @default.
- W2952172692 created "2019-06-27" @default.
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- W2952172692 date "2005-04-23" @default.
- W2952172692 modified "2023-09-27" @default.
- W2952172692 title "Klein polyhedra and lattices with positive norm minima" @default.
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