{"id":14805,"date":"2022-05-28T20:24:19","date_gmt":"2022-05-29T00:24:19","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14805"},"modified":"2026-06-09T10:43:13","modified_gmt":"2026-06-09T14:43:13","slug":"tr-177-representing-partial-orders-by-polygons-and-circles-in-the-plane-2","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/tr-177-representing-partial-orders-by-polygons-and-circles-in-the-plane-2\/","title":{"rendered":"TR-177: Representing Partial Orders by Polygons and Circles in the Plane"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-177: Representing Partial Orders by Polygons and Circles in the Plane\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1990\/\">Technical Report<\/a>&nbsp;<strong>TR-177<\/strong><br>July 1990<\/p>\n\n\n\n<h2 id=\"representing-partial-orders-by-polygons-and-circles-in-the-plane\" class=\"wp-block-heading\">Representing Partial Orders by Polygons and Circles in the Plane<\/h2>\n\n\n\n<p>Jeffrey B. Sidney &amp; Stuart J. Sidney<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>The representation of partial orders as containment orders for sets of geometric objects has attracted much attention over the last few years. New results for the cases of polygon ( n-gon) and circle orders are presented:<\/p>\n\n\n\n<p>( i) A result which relates the crossing number of a poset to the intersection number of polygon orders is given;<br>(ii) Two promising schemes for constructing circle orders for three-dimensional posets are shown not to work;<br>(iii) The Hiraguchi partial order is shown to be a circle order with circles of only two radii;<br>(iv) The question of which bipartite partial orders are circle orders is examined.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-177.pdf\">TR-177.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report&nbsp;TR-177July 1990 Representing Partial Orders by Polygons and Circles in the Plane Jeffrey B. Sidney &amp; Stuart J. Sidney Abstract The representation of partial orders as containment orders for sets of geometric objects has attracted much attention over the last few years. New results for the cases of polygon ( n-gon) and circle [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11906,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-14805","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14805"}],"version-history":[{"count":3,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14805\/revisions"}],"predecessor-version":[{"id":24536,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14805\/revisions\/24536"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11906"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14805"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}