{"id":14400,"date":"2024-08-26T14:22:28","date_gmt":"2024-08-26T19:22:28","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=14400"},"modified":"2024-10-25T12:09:50","modified_gmt":"2024-10-25T17:09:50","slug":"colloquium-aba-mbirika","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/colloquium-aba-mbirika\/","title":{"rendered":"Colloquium: aBa Mbirika & Morgan Fiebig"},"content":{"rendered":"

\"\"<\/h1>\n

A graphical approach to the Fibonacci sequence (Fn) n\u22650<\/em> modulo m<\/em> extended to the Lucas sequences (Un(p,q))n\u22650<\/em> and (Vn(P,q))n\u22650<\/em><\/h1>\n

aBa Mbirika<\/a> & Morgan Fiebig<\/a>
\nUniversity of Wisconsin – Eau Claire<\/p>\n

The goal of this talk is twofold: (1) extend theory on statistics in the Fibonacci and Lucas sequences modulo m to the Lucas sequences U :=(Un(p,q))n\u22650 and V :=(Vn(p,q)n 0, and (2) apply this theory to a novel graphical approach of U and V modulo m. The statistics we explore are the period \u03c0(m), entry point e(m), and order \u03c9(m) := pi(m)\/e(m). We generalize a wealth of known Fibonacci and Lucas statistical results to the U and V setting. Based on \u03c9(m), we describe behaviors shared by infinite families of nondegenerate U and V sequences with parameters q = \u00b1 1. In our graphical approach we place the cycle of repeating terms of the periods of U and V in a circle, and patterns which would otherwise be overlooked emerge. In particular, we exhibit some tantalizing examples in the following three sequence pairs: Fibonacci and Lucas, Pell and associated Pell, and, balancing and Lucas-balancing. Our proofs utilize results from primary sources ranging from the ground-breaking papers of Lucas in 1878 and Carmichael in 1913, to the seminal works of Wall in 1960 and Vinson in 1963, amongst others.<\/p>\n","protected":false},"excerpt":{"rendered":"

A graphical approach to the Fibonacci sequence (Fn) n\u22650 modulo m extended to the Lucas sequences (Un(p,q))n\u22650 and (Vn(P,q))n\u22650 aBa Mbirika & Morgan Fiebig University of Wisconsin – Eau Claire The goal of this talk is twofold: (1) extend theory …<\/p>\n","protected":false},"author":4217,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[41],"class_list":["post-14400","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-colloquia","cat_colloquia"],"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/colloquium-aba-mbirika\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Colloquium: aBa Mbirika & Morgan Fiebig\" \/>\n<meta property=\"og:description\" content=\"A graphical approach to the Fibonacci sequence (Fn) n\u22650 modulo m extended to the Lucas sequences (Un(p,q))n\u22650 and (Vn(P,q))n\u22650 aBa Mbirika & Morgan Fiebig University of Wisconsin – Eau Claire The goal of this talk is twofold: (1) extend theory …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/uwm.edu\/math\/event\/colloquium-aba-mbirika\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathematical Sciences\" \/>\n<meta property=\"article:modified_time\" content=\"2024-10-25T17:09:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/uwm.edu\/math\/wp-content\/uploads\/sites\/112\/2024\/08\/MBIRIKA-N-FIEBIG-BANNER.png\" \/>\n\t<meta property=\"og:image:width\" content=\"984\" \/>\n\t<meta property=\"og:image:height\" content=\"504\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-aba-mbirika\\\/\",\"url\":\"https:\\\/\\\/uwm.edu\\\/math\\\/event\\\/colloquium-aba-mbirika\\\/\",\"name\":\"Colloquium: aBa Mbirika & Morgan Fiebig - 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