{"id":1274,"date":"2017-10-04T14:27:04","date_gmt":"2017-10-04T18:27:04","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=1274"},"modified":"2026-03-19T08:10:27","modified_gmt":"2026-03-19T12:10:27","slug":"michael-albert-2","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/michael-albert-2\/","title":{"rendered":"Michael Albert"},"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<h1 class=\"wp-block-heading\">Michael Albert<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\">Monotonic sequence games<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract:<br>\nFrom a deck of cards labelled with the integers from 1 through $n$ two players take turns choosing a card and adding it to the right hand end of a row of cards. The game ends when there is a subsequence of $a$ cards in the row whose values form an ascending sequence, or of $d$ cards whose values form a descending sequence.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">I&#8217;ll discuss the &#8220;long run&#8221; (large $n$ for fixed $a$ and $d$) behaviour of this game and also some variants (e.g., when the deck of cards is $\\mathbb{Q}$.)<\/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":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1274","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1274","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=1274"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1274\/revisions"}],"predecessor-version":[{"id":3985,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/1274\/revisions\/3985"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}