{"id":2281,"date":"2012-04-18T23:57:54","date_gmt":"2012-04-18T23:57:54","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=2281"},"modified":"2012-04-18T23:57:54","modified_gmt":"2012-04-18T23:57:54","slug":"dependency-graph","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=2281","title":{"rendered":"Dependency graph"},"content":{"rendered":"

Some data regarding the dependency graph of the stacks project (on April 18, 2012).<\/p>\n

We think of the bottom of the graph (height 0) as the vertices whose tags correspond to results whose proofs do not refer to any other result. Height 1 is those which refer to a result of height 0. Etc. The maximum height is 78 which is attained by 06RD<\/a>. The next few are
\nHeight 77 : 06RA<\/a> 06RF<\/a> 07BE<\/a>
\nHeight 76 : 06QK<\/a> 06R9<\/a> 06RC<\/a> 06UF<\/a> 06UG<\/a> 07BA<\/a>
\nHeight 75 : 06QI<\/a> 06QJ<\/a> 06UD<\/a> 06UE<\/a> 06UI<\/a> 07B4<\/a> 07B9<\/a>
\nHeight 74 : 06MF<\/a> 06N3<\/a> 06QH<\/a> 07B3<\/a>
\nHeight 73 : 06G3<\/a> 06QG<\/a> 077A<\/a> 0783<\/a> 07AQ<\/a> 07B8<\/a> 07BC<\/a>
\nHeight 72 : 06MX<\/a> 06PL<\/a> 0771<\/a>
\nHeight 71 : 06MT<\/a> 06PK<\/a> 0765<\/a> 0782<\/a> 07AP<\/a>
\nHeight 70 : 06MR<\/a> 06PJ<\/a> 075Z<\/a> 0770<\/a> 0775<\/a>
\nHeight 69 : 050B<\/a> 06FI<\/a> 076Z<\/a> 0785<\/a><\/p>\n

The distribution (number of tags per height for height > 0) looks like this\"\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Some data regarding the dependency graph of the stacks project (on April 18, 2012). We think of the bottom of the graph (height 0) as the vertices whose tags correspond to results whose proofs do not refer to any other … Continue reading →<\/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":[1],"tags":[],"class_list":["post-2281","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2281"}],"version-history":[{"count":15,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2281\/revisions"}],"predecessor-version":[{"id":2297,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2281\/revisions\/2297"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}