Carleton University
Technical Report TR-206
April 1992
Enumeration Problems Relating to Dirichlet’s Theorem
Evangelos Kranakis & Michel Pocchiola
Abstract
We consider enumeration problems relating to Dirichlet’s theorem on the probability that two integers, taken at random, are relatively prime. We study weighted versions of the asymptotic number of lattice points inside a. domain 6 which a.re visible from the origin. This leads to a. uniform approach in the study of the asymptotic behavior of several problems in combinatorial and computational geometry like, the number of lines traversing at lea.st k vertices of a. cube or simplex, as well as the number of incidencies between a. set of points and lines and the complexity of the edge visibility region.