{"id":5107,"date":"2023-07-19T08:02:04","date_gmt":"2023-07-19T12:02:04","guid":{"rendered":"http:\/\/matroidunion.org\/?p=5107"},"modified":"2023-07-20T20:52:52","modified_gmt":"2023-07-21T00:52:52","slug":"online-talk-kevin-grace-2","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=5107","title":{"rendered":"Online Talk: Kevin Grace"},"content":{"rendered":"\n<p><strong>YouTube recording:<\/strong> <a href=\"https:\/\/www.youtube.com\/watch?v=qmlQeX5Oy0Q\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/www.youtube.com\/watch?v=qmlQeX5Oy0Q<\/a><\/p>\n\n\n\n<p><strong>Time: <\/strong>Thursday, July 20, 3pm ET<br><strong>Zoom: <\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/gatech.zoom.us\/j\/8802082683\" target=\"_blank\">https:\/\/gatech.zoom.us\/j\/8802082683<\/a><\/p>\n\n\n\n<p><strong>Speaker:&nbsp;<\/strong><a rel=\"noreferrer noopener\" href=\"https:\/\/kevingracemath.wordpress.com\/research\/\" target=\"_blank\">Kevin Grace<\/a>, Vanderbilt University<br><strong>Title: <\/strong>Some generalizations of the class of spikes<br><br><strong>Abstract: <\/strong>Spikes (also called tipless spikes in the matroid theory literature) form a well-known class of matroids that are important in the study of matroid connectivity. These matroids have the property that every pair of elements is contained in both a 4-element circuit and a 4-element cocircuit. We will present a family of generalizations of spikes, which we call (s, t)-spikes, with the property that every s-element subset of the ground set is contained in a 2s-element circuit and every t-element subset of the ground set is contained in a 2t-element cocircuit. We call this property the (s, 2s, t, 2t)-property. Our main result is that all sufficiently large matroids with the (s,2s, t, 2t)-property are (s, t)-spikes. This is joint work with Nick Brettell.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YouTube recording: https:\/\/www.youtube.com\/watch?v=qmlQeX5Oy0Q Time: Thursday, July 20, 3pm ETZoom: https:\/\/gatech.zoom.us\/j\/8802082683 Speaker:&nbsp;Kevin Grace, Vanderbilt UniversityTitle: Some generalizations of the class of spikes Abstract: Spikes (also called tipless spikes in the matroid theory literature) form a well-known class of matroids that are &hellip; <a href=\"https:\/\/matroidunion.org\/?p=5107\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":21,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11],"class_list":["post-5107","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\/5107","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\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5107"}],"version-history":[{"count":3,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/5107\/revisions"}],"predecessor-version":[{"id":5111,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/5107\/revisions\/5111"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}