{"id":{"repo_id":"wku-diss","oai_identifier":"oai:digitalcommons.wku.edu:theses-1671"},"canonical_url":"https://search.dev.ndltd.org/etd/wku-diss/oai:digitalcommons.wku.edu:theses-1671","repository":{"repo_id":"wku-diss","name":"Western Kentucky University","base_url":"https://digitalcommons.wku.edu/do/oai/"},"display":{"title":"Elgenvalues of Fibonacci-like Sequences","abstract":"The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = 1, and for each k, the ak's are either 0 or 1.","abstract_html":"The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = 1, and for each k, the ak's are either 0 or 1.","abstract_has_math":false,"creators":["Hurst, Elyssa"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics and Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001-05-01T07:00:00Z","date_published":"2001-05-01T07:00:00Z","updated_at":"2026-07-24T06:07:42Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/668","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hurst, Elyssa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics and Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/668"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = 1, and for each k, the ak's are either 0 or 1."]},{"key":"dc:title","label":"Title","values":["Elgenvalues of Fibonacci-like Sequences"]}]}],"canonical_facts":{"dc:creator":["Hurst, Elyssa"],"dc:description.abstract":["The familiar Fibonacci sequence 1,1,2,3,5,8,13,... can be described by the recurrence relation x(0) = 1, x(1) = 1, x(n) = x(n-1) + x(n-2). For this relation, as n → oo, x(n+1) → 1 +√5 x(n) 2 ' which is the familiar golden ratio. This value is also the dominant eigenvalue of the above recurrence relation. In this series, we consider the dominant eigenvalue of some Fibonacci-like sequence of the form x(n) = ∑n-1/k+1 ak Zk (n-k) where the Zk's are independent random variables with Zk = {+1 with probability p - 1 with probability q, with p + q = 1, and for each k, the ak's are either 0 or 1."],"dc:identifier":["https://digitalcommons.wku.edu/theses/668"],"dc:subject":["Mathematics"],"dc:title":["Elgenvalues of Fibonacci-like Sequences"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics and Computer Science"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:07:42Z"}