{"id":223,"date":"2011-11-21T01:09:52","date_gmt":"2011-11-21T00:09:52","guid":{"rendered":"http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/?page_id=223"},"modified":"2012-04-18T19:15:24","modified_gmt":"2012-04-18T18:15:24","slug":"numbers","status":"publish","type":"page","link":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/numbers\/","title":{"rendered":"Numbers"},"content":{"rendered":"<p>This page will be dedicated to experiments I have been doing with numerical semigroups, for several years&#8230;<\/p>\n<p>I am in a position to made public that the number of numerical semigroups with genus 55 is: <span style=\"color: #800080;\">1,142,140,736,859<\/span><\/p>\n<p>The highest number previously known is for genus 52. It is 266,815,155,103, about a quarter of the number of numerical semigroups of genus 55. It has been computed by Maria Bras-Amor\u00f3s and appears in an entry of the Neil J. A. Sloane&#8217;s <a href=\"http:\/\/www.research.att.com\/%7Enjas\/sequences\/A007323\">On-Line Encyclopedia of Integer Sequences<\/a>.<\/p>\n<p>The following nice images have been obtained using the number of numerical semigroups by genus and multiplicity. Other related images will be available here&#8230;<\/p>\n<p><a href=\"http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253.jpg\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-423\" title=\"image_3d_20111125\" src=\"http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253-300x212.jpg\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253-300x212.jpg 300w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253-1024x723.jpg 1024w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253-424x300.jpg 424w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_3d_201111253.jpg 1654w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>  &nbsp; <\/a><a href=\"http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243.jpg\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-medium wp-image-422\" title=\"image_111124\" src=\"http:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243-300x202.jpg\" alt=\"\" width=\"300\" height=\"202\" srcset=\"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243-300x202.jpg 300w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243-1024x690.jpg 1024w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243-445x300.jpg 445w, https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-content\/uploads\/2011\/11\/image_1111243.jpg 1172w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This page will be dedicated to experiments I have been doing with numerical semigroups, for several years&#8230; I am in a position to made public that the number of numerical semigroups with genus 55 is: 1,142,140,736,859 The highest number previously &hellip; <a href=\"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/numbers\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":7,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/pages\/223"}],"collection":[{"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/comments?post=223"}],"version-history":[{"count":18,"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/pages\/223\/revisions"}],"predecessor-version":[{"id":572,"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/pages\/223\/revisions\/572"}],"wp:attachment":[{"href":"https:\/\/cmup.fc.up.pt\/cmup\/mdelgado\/wp-json\/wp\/v2\/media?parent=223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}