{"id":579,"date":"2011-01-23T11:04:40","date_gmt":"2011-01-23T16:04:40","guid":{"rendered":"http:\/\/blog.carlrobitaille.org\/?p=579"},"modified":"2011-01-23T11:05:34","modified_gmt":"2011-01-23T16:05:34","slug":"eulers-partition-function-theory-finished","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=579","title":{"rendered":"Euler&#8217;s Partition Function Theory Finished"},"content":{"rendered":"<p><a href=\"http:\/\/blogs.plos.org\/badphysics\/2011\/01\/20\/ono\/\">The Language of Bad Physics: Finite formula found for partition numbers<\/a><\/p>\n<p>Via: <a href=\"http:\/\/science.slashdot.org\/story\/11\/01\/21\/2047229\/Eulers-Partition-Function-Theory-Finished?from=rss&amp;utm_source=feedburner&amp;utm_medium=feed&amp;utm_campaign=Feed%3A+Slashdot%2Fslashdot+%28Slashdot%29\">slashdot.org: Euler&#8217;s Partition Function Theory Finished<\/a><\/p>\n<blockquote><p>In this setting, a partition is a way of representing a natural number n as the sum of natural numbers (ie. for n = 3, we have three partitions, 3, 2 + 1, and 1 + 1 + 1, independent of order).  Thus, the partition function, p(n), represents the number of possible partitions of n.  So, p(3) = 3, p(4) = 5 (for n = 4, we have: 4, 3 + 1, 2 + 2, 2 + 1 + 1,  1 + 1 + 1 + 1) , etc..<\/p><\/blockquote>\n<blockquote><p>A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n.<\/p><\/blockquote>\n<blockquote><p>It seems that since Euler initially came up with his generating function, there haven\u2019t been major leaps in our understanding of partition numbers.<\/p>\n<p>Apparently that all changes tomorrow.  Ken Ono and colleagues, Jan Bruinier, Amanda Folsom and Zach Kent, will be announcing results that include a finite, algebraic formula for partition numbers thanks to the discovering that partitions are fractal. Well, so what does this mean, for partition numbers to be fractal?<\/p>\n<p>Ken Ono, in the press release:<\/p>\n<p>The sequences are all eventually periodic, and they repeat themselves over and over at precise intervals.<\/p><\/blockquote>\n<p>Voici le lien vers le <a href=\"http:\/\/www.aimath.org\/news\/partition\/folsom-kent-ono.pdf\">papier en format PDF<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Language of Bad Physics: Finite formula found for partition numbers Via: slashdot.org: Euler&#8217;s Partition Function Theory Finished In this setting, a partition is a way of representing a natural number n as the sum of natural numbers (ie. for &hellip; <a href=\"https:\/\/blog.carlrobitaille.org\/?p=579\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-579","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/579","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=579"}],"version-history":[{"count":2,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/579\/revisions"}],"predecessor-version":[{"id":582,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/579\/revisions\/582"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=579"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=579"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=579"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}