{"id":4064,"date":"2021-05-26T11:35:52","date_gmt":"2021-05-26T15:35:52","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4064"},"modified":"2021-05-31T17:30:37","modified_gmt":"2021-05-31T21:30:37","slug":"online-talk-daniel-slilaty","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4064","title":{"rendered":"Online Talk: Daniel Slilaty"},"content":{"rendered":"\n<p><strong>Monday, May 31,<\/strong> <strong>3pm ET<\/strong> (8pm BST, 7am Tue NZST)<br \/><strong><a href=\"http:\/\/www.daniel-slilaty.xyz\/\">Daniel Slilaty<\/a><\/strong>, Wright State University<br \/><strong>Orientations of golden-mean matroids<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/youtu.be\/kD1M0Gth5O0\">https:\/\/youtu.be\/kD1M0Gth5O0<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><b><\/b><strong>Abstract:<\/strong><\/h5>\n<p>Tutte proved that a binary matroid is representable over some field of characteristic other than 2 if and only if the matroid is regular. His result inspired the discovery of analogs for $GF(3)$-representable matroids by Whittle, $GF(4)$-representable matroids by Vertigan as well as Pendavingh and Van Zwam, and $GF(5)$-representable matroids by Pendavingh and Van Zwam.<\/p>\n<p>Bland and Las Vergnas proved that a binary matroid&#8217;s orientations correspond to its regular representations. (Minty&#8217;s result on digraphoids is closely related.) Lee and Scobee proved that a $GF(3)$-representable matroid&#8217;s orientations correspond to its dyadic representations. In this talk we will explore orientations of $GF(4)$-representable matroids. A natural partial field to use is the golden-mean partial field; however, not every orientation of a $GF(4)$-representable matroid comes from a golden-mean representation. For example, $U_{3,6}$ has 372 orientations but only 12 of them come from golden-mean representations. We will give a combinatorial characterization of those orientations of $GF(4)$-representable matroids which do come from golden-mean representations and show that these orientations correspond one-to-one to the golden-mean representations.<\/p>\n<p>Joint work with Jakayla Robbins.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Monday, May 31, 3pm ET (8pm BST, 7am Tue NZST)Daniel Slilaty, Wright State UniversityOrientations of golden-mean matroids YouTube: https:\/\/youtu.be\/kD1M0Gth5O0 \u00a0 Abstract: Tutte proved that a binary matroid is representable over some field of characteristic other than 2 if and only &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4064\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":20,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-4064","post","type-post","status-publish","format-standard","hentry","category-matroids","tag-online-talks"],"_links":{"self":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4064","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4064"}],"version-history":[{"count":2,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4064\/revisions"}],"predecessor-version":[{"id":4069,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4064\/revisions\/4069"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4064"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4064"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}