{"id":4544,"date":"2022-01-12T15:55:57","date_gmt":"2022-01-12T20:55:57","guid":{"rendered":"http:\/\/matroidunion.org\/?p=4544"},"modified":"2022-01-20T01:17:45","modified_gmt":"2022-01-20T06:17:45","slug":"online-talk-mehtaab-sawhney","status":"publish","type":"post","link":"https:\/\/matroidunion.org\/?p=4544","title":{"rendered":"Online Talk: Mehtaab Sawhney"},"content":{"rendered":"\n<p><strong>Tuesday, Jan 18,<\/strong> <strong>3pm ET<\/strong> (8pm GMT, 9am Wed NZDT)<br \/><strong><a href=\"http:\/\/www.mit.edu\/~msawhney\/\">Mehtaab Sawhney<\/a><\/strong>, MIT<br \/><strong>Enumerating Matroids and Linear Spaces<\/strong><\/p>\n<div><strong>YouTube: <\/strong><a href=\"https:\/\/youtu.be\/BVq-iBDqz48\">https:\/\/youtu.be\/BVq-iBDqz48<\/a><\/div>\n<h5>\u00a0<\/h5>\n<h5><strong>Abstract:<\/strong><\/h5>\n<h5>We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2\/6}$, where $c=e^{\\sqrt 3\/2-3}(1+\\sqrt 3)\/2$. This is the final piece of the puzzle for enumerating fixed-rank matroids at this level of accuracy: there are exact formulas for enumeration of rank-1 and rank-2 matroids, and it was recently proved by van der Hofstad, Pendavingh, and van der Pol that for constant $r\\ge 4$ there are $(e^{1-r}n+o(n))^{n^{r-1}\/r!}$ rank-$r$ matroids on a ground set of size $n$.\u00a0In our proof, we introduce a new approach for bounding the number of clique decompositions of a complete graph, using quasirandomness instead of the so-called entropy method that is common in this area.<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>Tuesday, Jan 18, 3pm ET (8pm GMT, 9am Wed NZDT)Mehtaab Sawhney, MITEnumerating Matroids and Linear Spaces YouTube: https:\/\/youtu.be\/BVq-iBDqz48 \u00a0 Abstract: We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids &hellip; <a href=\"https:\/\/matroidunion.org\/?p=4544\">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-4544","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\/4544","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=4544"}],"version-history":[{"count":2,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4544\/revisions"}],"predecessor-version":[{"id":4561,"href":"https:\/\/matroidunion.org\/index.php?rest_route=\/wp\/v2\/posts\/4544\/revisions\/4561"}],"wp:attachment":[{"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matroidunion.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}