{"id":49,"date":"2010-05-12T16:32:34","date_gmt":"2010-05-12T16:32:34","guid":{"rendered":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/?p=49"},"modified":"2010-05-12T16:33:27","modified_gmt":"2010-05-12T16:33:27","slug":"new-data","status":"publish","type":"post","link":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/?p=49","title":{"rendered":"New data"},"content":{"rendered":"<p>I ran the Minkowski ansatz for all 4319 3-dimensional reflexive polytopes, calculating the first 100 power series coefficients of the principal period for each of them.\u00a0 The results were as follows.<\/p>\n<p>3025 of the polytopes had a non-empty list of Minkowski polynomials, and 670 of them had more than one Minkowksi polynomial.<\/p>\n<p>There were 165 distinct sequences of power series coefficients.\u00a0 I then looked for differential operators <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/a66\/a669ea21211537830afcea8d9d679d3d-ffffff-000000-0.png' alt='P(t,D)' title='P(t,D)' class='latex' \/> annilihating the principal period such that <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/a66\/a669ea21211537830afcea8d9d679d3d-ffffff-000000-0.png' alt='P(t,D)' title='P(t,D)' class='latex' \/> has degree <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/8d9\/8d9c307cb7f3c4a32822a51922d1ceaa-ffffff-000000-0.png' alt='N' title='N' class='latex' \/> in <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/f62\/f623e75af30e62bbd73d6df5b50bb7b5-ffffff-000000-0.png' alt='D' title='D' class='latex' \/> and <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/4b4\/4b43b0aee35624cd95b910189b3dc231-ffffff-000000-0.png' alt='r' title='r' class='latex' \/> in <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/e35\/e358efa489f58062f10dd7316b65649e-ffffff-000000-0.png' alt='t' title='t' class='latex' \/>, where <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/0a2\/0a250f9b1ee0c3c4f41dcd7736f4292c-ffffff-000000-0.png' alt='N \\leq 5' title='N \\leq 5' class='latex' \/> and <img src='http:\/\/coates.ma.ic.ac.uk\/fanosearch\/wp-content\/latex\/4d7\/4d7867edc3042cca66a50780f8857a78-ffffff-000000-0.png' alt='(N+1)(r+1)\\leq 90.' title='(N+1)(r+1)\\leq 90.' class='latex' \/>\u00a0 The results were:<\/p>\n<pre>N=3:\t23 examples in total\r\n\r\nr=2:\t3 examples\r\nr=3:\t2 examples\r\nr=4:\t18 examples\r\n\r\nN=4:\t49 examples in total\r\n\r\nr=7:\t5 examples\r\nr=8:\t3 examples\r\nr=9:\t14 examples\r\nr=10:\t27 examples\r\n\r\nN=5:\t10 examples in total\r\n\r\nr=11:\t1 example\r\nr=12:\t2 examples\r\nr=13:\t0 examples\r\nr=14:\t7 examples<\/pre>\n<p>So in particular we found 23 D3 forms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I ran the Minkowski ansatz for all 4319 3-dimensional reflexive polytopes, calculating the first 100 power series coefficients of the principal period for each of them.\u00a0 The results were as follows. 3025 of the polytopes had a non-empty list of Minkowski polynomials, and 670 of them had more than one Minkowksi polynomial. There were 165 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[5],"class_list":["post-49","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-data"],"_links":{"self":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/49","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=49"}],"version-history":[{"count":8,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/49\/revisions"}],"predecessor-version":[{"id":57,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=\/wp\/v2\/posts\/49\/revisions\/57"}],"wp:attachment":[{"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=49"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=49"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/coates.ma.ic.ac.uk\/fanosearch\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=49"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}