{"id":83476,"date":"2022-12-24T17:29:30","date_gmt":"2022-12-24T14:29:30","guid":{"rendered":"https:\/\/azbuki.bg\/?p=83476"},"modified":"2025-07-08T09:44:36","modified_gmt":"2025-07-08T06:44:36","slug":"sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon","status":"publish","type":"post","link":"https:\/\/philosophy.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/","title":{"rendered":"Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon"},"content":{"rendered":"<p><strong>Ivaylo Kortezov<\/strong><br \/>\n<em>Institute of Mathematics and Informatics \u2013 BAS, Sofia, Bulgaria<\/em><\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2022-6-4-set\" target=\"_blank\" rel=\"noopener noreferrer\">https:\/\/doi.org\/10.53656\/math2022-6-4-set<\/a><\/p>\n<p><strong>Abstract.<\/strong> The paper deals with counting the sets of non-self-intersecting paths whose nodes form a partitioning of the set of vertices of a given convex polygon. There turn to exist compact formulae when the magnitude of these sets is fixed. Some of these formulae provide new properties for some of the entries of the On-line Encyclopedia of Integer Sequences, while others generate new entries therein.<br \/>\n<em>Keywords:<\/em> enumerative combinatorics; non-self-intersecting paths; convex polygons; OEIS<\/p>\n<a href=\"https:\/\/philosophy.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>Ivaylo Kortezov Institute of Mathematics and Informatics \u2013 BAS, Sofia, Bulgaria https:\/\/doi.org\/10.53656\/math2022-6-4-set Abstract. The paper deals with counting the sets of non-self-intersecting paths whose nodes form a partitioning of the set of vertices of a given convex polygon. There turn to exist compact formulae when the magnitude of these sets is fixed. Some of these [&hellip;]<\/p>","protected":false},"author":124332423426818,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":{"subtitle":"","format":"standard","video":"","gallery":"","source_name":"","source_url":"","via_name":"","via_url":"","override_template":"0","override":[{"single_blog_custom":"","parallax":"0","fullscreen":"0","sidebar":"","second_sidebar":"","sticky_sidebar":"0","share_position":"","share_float_style":"","show_share_counter":"0","show_view_counter":"0","show_featured":"0","show_post_meta":"0","show_post_author":"0","show_post_author_image":"0","show_post_date":"0","post_date_format":"","post_date_format_custom":"","show_post_category":"0","show_post_reading_time":"0","post_reading_time_wpm":"","show_post_tag":"0","show_prev_next_post":"0","show_popup_post":"0","number_popup_post":"1","show_author_box":"0","show_post_related":"0","show_inline_post_related":"0"}],"override_image_size":"0","image_override":[{"single_post_thumbnail_size":"","single_post_gallery_size":""}],"trending_post":"0","trending_post_position":"","trending_post_label":""},"jnews_primary_category":{"id":""}},"categories":[1],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Ivaylo Kortezov Institute of Mathematics and Informatics \u2013 BAS, Sofia, Bulgaria https:\/\/doi.org\/10.53656\/math2022-6-4-set Abstract. The paper deals with counting the sets of non-self-intersecting paths whose nodes form a partitioning of the set of vertices of a given convex polygon. There turn to exist compact formulae when the magnitude of these sets is fixed. Some of these [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-12-24T14:29:30+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-08T06:44:36+00:00\" \/>\n<meta name=\"author\" content=\"v.genkov@azbuki.bg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"v.genkov@azbuki.bg\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\"},\"author\":{\"name\":\"v.genkov@azbuki.bg\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/92cc38d6a11fb032bf6299efd22a71c5\"},\"headline\":\"Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon\",\"datePublished\":\"2022-12-24T14:29:30+00:00\",\"dateModified\":\"2025-07-08T06:44:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\"},\"wordCount\":128,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\",\"url\":\"https:\/\/strategies.azbuki.bg\/en\/uncategorized\/sets-of-non-self-intersecting-paths-connecting-the-vertices-of-a-convex-polygon\/\",\"name\":\"Sets of Non-Self-Intersecting Paths Connecting the Vertices of a Convex Polygon - 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