Farey Statistics in Time n2/3 and Counting Primitive Lattice Points in Polygons
Abstract
We present algorithms for computing ranks and order statistics in the Farey sequence, taking time O (n2/3). This improves on the recent algorithms of Pawlewicz [European Symp. Alg. 2007], running in time O (n3/4). We also initiate the study of a more general algorithmic problem: counting primitive lattice points in planar shapes.
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