Dr. Michael DiPasquale, Colorado State University.<\/p>\n\n\n\n
Title<\/strong>: Extending Wilf’s Conjecture<\/p>\n\n\n\n Abstract<\/strong>: Suppose $a_1,a_2,\\ldots,a_n$ is a set of positive integers which are relatively prime. The set of all integers which can be written as a non-negative integer combination of $a_1,\\ldots,a_n$ is called a numerical semigroup. The non-negative integers which are not in the numerical semigroup is called the set of holes of the semigroup. It is known that the set of holes of a numerical semigroup is finite, and the largest hole is called the conductor. In a four-page note in the American Mathematical Monthly in 1978, Herbert Wilf asked a question about the density of the set of holes of a numerical semigroup in the interval from zero through the conductor. This question is still widely open and has become known as Wilf’s conjecture. We will discuss this conjecture and a recent extension of it to higher dimensions which is joint work with C. Cisto, G. Failla, Z. Flores, C. Peterson, and R. Utano.<\/p>\n","protected":false},"excerpt":{"rendered":" Dr. Michael DiPasquale, Colorado State University. Title: Extending Wilf’s Conjecture Abstract: Suppose $a_1,a_2,\\ldots,a_n$ is a set of positive integers which are relatively prime. The set of all integers which can be written as a non-negative integer combination of $a_1,\\ldots,a_n$ is called a numerical semigroup. The non-negative integers which are not in the numerical semigroup is […]<\/p>\n","protected":false},"author":1211,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-551","post","type-post","status-publish","format-standard","hentry","category-spring-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-8T","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/users\/1211"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=551"}],"version-history":[{"count":3,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/551\/revisions"}],"predecessor-version":[{"id":555,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/551\/revisions\/555"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}