{"id":"https://openalex.org/W7160606644","doi":"https://doi.org/10.1093/jigpal/jzag019","title":"Fibonacci-based Pascal-like matrices with double factorial binomial structure","display_name":"Fibonacci-based Pascal-like matrices with double factorial binomial structure","publication_year":2026,"publication_date":"2026-03-31","ids":{"openalex":"https://openalex.org/W7160606644","doi":"https://doi.org/10.1093/jigpal/jzag019"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzag019","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jigpal/jzag019","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1093/jigpal/jzag019","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":true,"raw_author_name":"Can Kizilate\u015f","raw_affiliation_strings":["Department of Mathematics , Faculty of Science, Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Science, Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"last","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":"Nazlihan Terzio\u011flu","raw_affiliation_strings":["Graduate School of Natural and Applied Sciences , Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Natural and Applied Sciences , Zonguldak B\u00fclent Ecevit University, 67100, Zonguldak, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018343835"],"corresponding_institution_ids":["https://openalex.org/I3017902709"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":{"value":4151,"currency":"USD","value_usd":4151},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.67500218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.7731000185012817,"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":0.7731000185012817,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.18440000712871552,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.00430000014603138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.8574000000953674},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.83160001039505},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.6972000002861023},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.6798999905586243},{"id":"https://openalex.org/keywords/factorial","display_name":"Factorial","score":0.6662999987602234},{"id":"https://openalex.org/keywords/pascal-matrix","display_name":"Pascal matrix","score":0.516700029373169},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.5110999941825867},{"id":"https://openalex.org/keywords/multinomial-distribution","display_name":"Multinomial distribution","score":0.4839000105857849},{"id":"https://openalex.org/keywords/central-binomial-coefficient","display_name":"Central binomial coefficient","score":0.4747999906539917},{"id":"https://openalex.org/keywords/binomial-approximation","display_name":"Binomial approximation","score":0.3944999873638153}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8622000217437744},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.8574000000953674},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.83160001039505},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.6972000002861023},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.6798999905586243},{"id":"https://openalex.org/C183763347","wikidata":"https://www.wikidata.org/wiki/Q120976","display_name":"Factorial","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5300999879837036},{"id":"https://openalex.org/C183357087","wikidata":"https://www.wikidata.org/wiki/Q7141739","display_name":"Pascal matrix","level":5,"score":0.516700029373169},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.5110999941825867},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C134087691","wikidata":"https://www.wikidata.org/wiki/Q1045966","display_name":"Central binomial coefficient","level":4,"score":0.4747999906539917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4496000111103058},{"id":"https://openalex.org/C9209722","wikidata":"https://www.wikidata.org/wiki/Q4914487","display_name":"Binomial approximation","level":4,"score":0.3944999873638153},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C3634175","wikidata":"https://www.wikidata.org/wiki/Q2503280","display_name":"Lucas number","level":3,"score":0.38679999113082886},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C75608658","wikidata":"https://www.wikidata.org/wiki/Q44395","display_name":"Pascal (unit)","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.32170000672340393},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.30379998683929443},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29319998621940613},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/jigpal/jzag019","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jigpal/jzag019","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1093/jigpal/jzag019","is_oa":true,"landing_page_url":"https://doi.org/10.1093/jigpal/jzag019","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1554890859","https://openalex.org/W2046982222","https://openalex.org/W2090018201","https://openalex.org/W2330608158","https://openalex.org/W3080245800","https://openalex.org/W4212799367","https://openalex.org/W4251943764","https://openalex.org/W4387309367"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,70],"introduce":[5],"and":[6,40,52,81,93,115,119,128,144],"investigate":[7],"a":[8,45,72,99],"new":[9,100],"class":[10],"of":[11,62,84,134],"Pascal-like":[12],"matrices":[13,130],"constructed":[14],"using":[15],"double":[16,36],"F-factorial":[17,37],"binomial":[18,38,127],"coefficients,":[19],"in":[20,140],"which":[21],"the":[22,29,35,60,111,132],"standard":[23],"factorial":[24,54],"function":[25],"is":[26],"replaced":[27],"by":[28,76],"Fibonacci":[30,51,135],"factorial.":[31],"We":[32,96],"first":[33],"define":[34,98],"coefficient":[39],"employ":[41],"it":[42],"to":[43,109],"generate":[44],"bivariate":[46],"polynomial":[47],"sequence":[48],"incorporating":[49],"both":[50],"Lucas":[53],"terms.":[55],"Fundamental":[56],"recurrence":[57],"relations":[58],"for":[59],"coefficients":[61],"these":[63,68],"polynomials":[64],"are":[65],"established.":[66],"Using":[67],"relations,":[69],"construct":[71],"$F$-Pascal-like":[73],"matrix,":[74,114],"denoted":[75],"$P_{t}\\left":[77],"(":[78,105],"u,v\\right":[79],")_{F},$":[80,107],"derive":[82],"several":[83],"its":[85,117],"algebraic":[86],"properties,":[87],"including":[88],"matrix":[89,102,145],"factorization,":[90],"power":[91],"identities,":[92],"determinant-trace":[94],"relationships.":[95],"further":[97],"functional":[101],"$Q_{t,\\lambda":[103],"}\\left":[104],"x,y\\right":[106],"referred":[108],"as":[110],"$F$":[112],"-Pascal-like":[113],"include":[116],"additive":[118],"product":[120],"properties.":[121],"The":[122],"proposed":[123],"constructions":[124],"extend":[125],"classical":[126],"Pascal":[129],"within":[131],"framework":[133],"analysis,":[136],"providing":[137],"potential":[138],"applications":[139],"combinatorics,":[141],"number":[142],"theory,":[143],"theory.":[146]},"counts_by_year":[],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2026-05-09T00:00:00"}