{"id":"https://openalex.org/W4402984748","doi":"https://doi.org/10.3390/axioms13100677","title":"New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components","display_name":"New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components","publication_year":2024,"publication_date":"2024-09-30","ids":{"openalex":"https://openalex.org/W4402984748","doi":"https://doi.org/10.3390/axioms13100677"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13100677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100677","pdf_url":"https://www.mdpi.com/2075-1680/13/10/677/pdf?version=1727706963","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/10/677/pdf?version=1727706963","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018343835","display_name":"Can K\u0131z\u0131late\u015f","orcid":"https://orcid.org/0000-0002-7958-4226"},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Can K\u0131z\u0131late\u015f","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak 67100, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-7958-4226","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak 67100, T\u00fcrkiye","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032108378","display_name":"Wei\u2013Shih Du","orcid":"https://orcid.org/0000-0001-8996-2270"},"institutions":[{"id":"https://openalex.org/I135551196","display_name":"National Kaohsiung Normal University","ror":"https://ror.org/04tsc8g87","country_code":"TW","type":"education","lineage":["https://openalex.org/I135551196"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Wei-Shih Du","raw_affiliation_strings":["Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan"],"raw_orcid":"https://orcid.org/0000-0001-8996-2270","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan","institution_ids":["https://openalex.org/I135551196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048652181","display_name":"Nazl\u0131han Terzio\u011flu","orcid":"https://orcid.org/0000-0002-0408-8797"},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Nazl\u0131han Terzio\u011flu","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak 67100, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-0408-8797","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zonguldak B\u00fclent Ecevit University, Zonguldak 67100, T\u00fcrkiye","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023287231","display_name":"Ren-Chuen Chen","orcid":"https://orcid.org/0000-0002-5956-122X"},"institutions":[{"id":"https://openalex.org/I135551196","display_name":"National Kaohsiung Normal University","ror":"https://ror.org/04tsc8g87","country_code":"TW","type":"education","lineage":["https://openalex.org/I135551196"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ren-Chuen Chen","raw_affiliation_strings":["Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-5956-122X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824004, Taiwan","institution_ids":["https://openalex.org/I135551196"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032108378"],"corresponding_institution_ids":["https://openalex.org/I135551196"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.2482,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.53702532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"10","first_page":"677","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9506000280380249,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9200999736785889,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.8830603361129761},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.8198823928833008},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7109314203262329},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6095852255821228},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5426225662231445},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5275378227233887},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4266927242279053},{"id":"https://openalex.org/keywords/half-integer","display_name":"Half-integer","score":0.4170699715614319},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.4103473424911499},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3937697112560272},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35233670473098755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34283944964408875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1995689868927002},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10360074043273926},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.09327071905136108},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.07167631387710571},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05810609459877014}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8830603361129761},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8198823928833008},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7109314203262329},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6095852255821228},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5426225662231445},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5275378227233887},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4266927242279053},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.4170699715614319},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.4103473424911499},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3937697112560272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35233670473098755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34283944964408875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1995689868927002},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10360074043273926},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.09327071905136108},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.07167631387710571},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05810609459877014},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13100677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100677","pdf_url":"https://www.mdpi.com/2075-1680/13/10/677/pdf?version=1727706963","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a4c964c66c5941f4b5e4f4bf6c6cbc71","is_oa":false,"landing_page_url":"https://doaj.org/article/a4c964c66c5941f4b5e4f4bf6c6cbc71","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 10, p 677 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13100677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13100677","pdf_url":"https://www.mdpi.com/2075-1680/13/10/677/pdf?version=1727706963","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402984748.pdf","grobid_xml":"https://content.openalex.org/works/W4402984748.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W602384322","https://openalex.org/W1688854663","https://openalex.org/W2044491992","https://openalex.org/W2097583789","https://openalex.org/W2283945594","https://openalex.org/W2321807852","https://openalex.org/W2332156326","https://openalex.org/W2599636076","https://openalex.org/W2899378296","https://openalex.org/W2979350905","https://openalex.org/W3013180339","https://openalex.org/W3034202079","https://openalex.org/W3094017063","https://openalex.org/W3126930083","https://openalex.org/W3134465901","https://openalex.org/W3170428231","https://openalex.org/W4240644230","https://openalex.org/W4280588756","https://openalex.org/W4293097764","https://openalex.org/W4300054450","https://openalex.org/W4300605813","https://openalex.org/W4366759795","https://openalex.org/W4392375511","https://openalex.org/W4403206337","https://openalex.org/W6769458482","https://openalex.org/W6774750590"],"related_works":["https://openalex.org/W2013211436","https://openalex.org/W199458103","https://openalex.org/W4302160578","https://openalex.org/W2369612463","https://openalex.org/W2068305078","https://openalex.org/W3153521509","https://openalex.org/W2048541553","https://openalex.org/W2366105249","https://openalex.org/W2053241624","https://openalex.org/W2044496489"],"abstract_inverted_index":{"In":[0,65],"this":[1],"paper,":[2],"by":[3,77],"using":[4,78],"q-integers":[5],"and":[6,35,56],"higher-order":[7,14],"generalized":[8,15],"Fibonacci":[9,16],"numbers,":[10],"we":[11,67],"define":[12],"the":[13],"quaternions":[17,36,60,76],"with":[18,61],"q-integer":[19],"components.":[20],"We":[21,38],"give":[22],"some":[23,43,69],"special":[24,81],"cases":[25],"of":[26,59,75],"these":[27,73],"newly":[28],"established":[29],"quaternions.":[30],"This":[31],"article":[32],"examines":[33],"q-calculus":[34],"together.":[37],"obtain":[39,68],"a":[40,46,49],"Binet-like":[41],"formula,":[42],"new":[44,70,80],"identities,":[45],"generating":[47,54],"function,":[48,55],"recurrence":[50],"relation,":[51],"an":[52],"exponential":[53],"sum":[57],"properties":[58],"quantum":[62],"integer":[63],"coefficients.":[64],"addition,":[66],"identities":[71],"for":[72],"types":[74],"three":[79],"matrices.":[82]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}