{"id":251,"date":"2019-03-22T15:28:15","date_gmt":"2019-03-22T20:28:15","guid":{"rendered":"http:\/\/blogs.acu.edu\/mu_sigma\/?p=251"},"modified":"2019-03-22T15:28:15","modified_gmt":"2019-03-22T20:28:15","slug":"problem-15-march-22-permutations-everywhere","status":"publish","type":"post","link":"https:\/\/blogs.acu.edu\/mu_sigma\/2019\/03\/22\/problem-15-march-22-permutations-everywhere\/","title":{"rendered":"Problem 15 &#8211; March 22 &#8211;  Permutations Everywhere"},"content":{"rendered":"<p><span style=\"font-size: xx-large\"><b>Permutations Everywhere<\/b><\/span><\/p>\n<p>If <b>A<\/b> = {<i>a<sub>ij<\/sub><\/i> } is a symmetric (i.e., <i>a<sub>ij<\/sub><\/i> = <i>a<sub>ji<\/sub><\/i>) <i>n<\/i> by <i>n<\/i> matrix with <i>n<\/i> odd, and each row of the matrix is a permutation of the integers 1, 2, 3, &#8230; , <i>n<\/i>, prove that the main diagonal of <b>A<\/b> is also a permutation of 1, 2, 3, &#8230; , <i>n<\/i>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Permutations Everywhere If A = {aij } is a symmetric (i.e., aij = aji) n by n matrix with n odd, and each row of the matrix is a permutation of the integers 1, 2, 3, &#8230; , n, prove that the main diagonal of A is also a permutation of 1, 2, 3, &#8230; [&hellip;]<\/p>\n","protected":false},"author":130,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[181534],"tags":[],"class_list":["post-251","post","type-post","status-publish","format-standard","hentry","category-problem-of-the-week"],"_links":{"self":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/251","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/users\/130"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/comments?post=251"}],"version-history":[{"count":1,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/251\/revisions"}],"predecessor-version":[{"id":252,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/posts\/251\/revisions\/252"}],"wp:attachment":[{"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/media?parent=251"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/categories?post=251"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.acu.edu\/mu_sigma\/wp-json\/wp\/v2\/tags?post=251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}