{"id":804,"date":"2018-03-18T11:57:37","date_gmt":"2018-03-18T15:57:37","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/alexb\/?p=804"},"modified":"2026-03-19T08:12:39","modified_gmt":"2026-03-19T12:12:39","slug":"prellberg_3_20_18","status":"publish","type":"post","link":"https:\/\/people.clas.ufl.edu\/alexb\/2018\/03\/18\/prellberg_3_20_18\/","title":{"rendered":"Thomas Prellberg"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h2 class=\"wp-block-heading\">The Combinatorics of the leading root of Ramanujan&#8217;s function<\/h2>\n\n\n\n<h4 class=\"wp-block-heading\">When\/Where:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">March 20, 2018, 3:00 &#8212; 3:50 pm at LIT 368.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Abstract:<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">I consider the leading root \\(x_0(q)\\) of Ramanujan&#8217;s function (or \\(q\\)-Airy function) \\(\\sum\\limits_{n=0}^\\infty\\frac{(-x)^nq^{n^2}}{(1-q)(1-q^2)\\ldots(1-q^n)}\\). I prove that its formal power series expansion<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">\\(qx_0(-q)=1+q+q^2+2q^3+4q^4+8q^5+\\ldots\\)<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">has positive integer-valued coefficients, by giving an explicit combinatorial interpretation of these numbers in terms of trees whose vertices are decorated with polyominos.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Similar results are also obtained for the leading roots of the partial Theta function and the Painleve Airy function.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":331,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"featured_post":"off","footnotes":"","_links_to":"","_links_to_target":""},"categories":[5],"tags":[],"class_list":["post-804","post","type-post","status-publish","format-standard","hentry","category-nts-posting"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/804","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/users\/331"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/comments?post=804"}],"version-history":[{"count":3,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/804\/revisions"}],"predecessor-version":[{"id":1143,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/posts\/804\/revisions\/1143"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/media?parent=804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/categories?post=804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alexb\/wp-json\/wp\/v2\/tags?post=804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}