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- W2010667816 abstract "The linear action of SL(n, ℤ+) induces lattice partitions on the (n − 1)-dimensional simplex †n−1. The notion of Farey partition raises naturally from a matricial interpretation of the arithmetical Farey sequence of order r. Such sequence is unique and, consequently, the Farey partition of order r on A 1 is unique. In higher dimension no generalized Farey partition is unique. Nevertheless in dimension 3 the number of triangles in the various generalized Farey partitions is always the same which fails to be true in dimension n > 3. Concerning Diophantine approximations, it turns out that the vertices of an n-dimensional Farey partition of order r are the radial projections of the lattice points in ℤ+n ∩ [0, r]n whose coordinates are relatively prime. Moreover, we obtain sequences of multidimensional Farey partitions which converge pointwisely." @default.
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- W2010667816 date "2006-09-01" @default.
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- W2010667816 title "Multidimensional Farey partitions" @default.
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- W2010667816 doi "https://doi.org/10.1016/s0019-3577(06)80043-1" @default.
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