{"id":15042,"date":"2022-06-16T20:10:48","date_gmt":"2022-06-17T00:10:48","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15042"},"modified":"2022-06-16T20:10:48","modified_gmt":"2022-06-17T00:10:48","slug":"tr-206-enumeration-problems-relating-to-dirichlets-theorem","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1992\/tr-206-enumeration-problems-relating-to-dirichlets-theorem\/","title":{"rendered":"TR-206: Enumeration Problems Relating to Dirichlet&#8217;s Theorem"},"content":{"rendered":"<p>Carleton University<br \/>\n<a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1992\/\">Technical Report<\/a> <strong>TR-206<\/strong><br \/>\nApril 1992<\/p>\n<h2 class=\"tr_t1\">Enumeration Problems Relating to Dirichlet&#8217;s Theorem<\/h2>\n<div class=\"tr_t3\">Evangelos Kranakis &amp; Michel Pocchiola<\/div>\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n<p>We consider enumeration problems relating to Dirichlet&#8217;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.<\/p>\n<div><\/div>\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/TR-206.pdf\">TR-206.pdf<\/a><\/p>\n<p><script src=\"moz-extension:\/\/c5a13a0c-07c2-4cc2-a1b8-4c3d783074b0\/js\/app.js\" type=\"text\/javascript\"><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-206 April 1992 Enumeration Problems Relating to Dirichlet&#8217;s Theorem Evangelos Kranakis &amp; Michel Pocchiola Abstract We consider enumeration problems relating to Dirichlet&#8217;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 [&hellip;]<\/p>\n","protected":false},"author":49,"featured_media":0,"parent":11910,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":"","_links_to":"","_links_to_target":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>TR-206: Enumeration Problems Relating to Dirichlet&#039;s Theorem - School of Computer Science<\/title>\n<meta name=\"description\" content=\"Carleton University Technical Report TR-206 April 1992 Enumeration Problems Relating to Dirichlet&#039;s Theorem Evangelos Kranakis &amp; 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