{"id":"https://openalex.org/W3210961220","doi":"https://doi.org/10.3390/sym13112075","title":"Distance Fibonacci Polynomials by Graph Methods","display_name":"Distance Fibonacci Polynomials by Graph Methods","publication_year":2021,"publication_date":"2021-11-03","ids":{"openalex":"https://openalex.org/W3210961220","doi":"https://doi.org/10.3390/sym13112075","mag":"3210961220"},"language":"en","primary_location":{"id":"doi:10.3390/sym13112075","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112075","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2075/pdf?version=1635910925","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/11/2075/pdf?version=1635910925","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068540047","display_name":"Dominik Strza\u0142ka","orcid":"https://orcid.org/0000-0002-8887-4321"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Dominik Strza\u0142ka","raw_affiliation_strings":["Faculty of Electrical and Computer Engineering, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-8887-4321","affiliations":[{"raw_affiliation_string":"Faculty of Electrical and Computer Engineering, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I111664937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028482001","display_name":"S. Wolski","orcid":"https://orcid.org/0000-0002-8968-0959"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"S\u0142awomir Wolski","raw_affiliation_strings":["Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-8968-0959","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I111664937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024032357","display_name":"Andrzej W\u0142och","orcid":"https://orcid.org/0000-0003-1789-6280"},"institutions":[{"id":"https://openalex.org/I111664937","display_name":"Rzesz\u00f3w University of Technology","ror":"https://ror.org/056xse072","country_code":"PL","type":"education","lineage":["https://openalex.org/I111664937"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej W\u0142och","raw_affiliation_strings":["Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0003-1789-6280","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Aleja Powsta\u0144c\u00f3w Warszawy 12, 35-959 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I111664937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024032357"],"corresponding_institution_ids":["https://openalex.org/I111664937"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5247,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.65513275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"13","issue":"11","first_page":"2075","last_page":"2075"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.958899974822998,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.954800009727478,"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/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.8879892826080322},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.7576048970222473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7319692373275757},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5839171409606934},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.4659024178981781},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4528660178184509},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4317152202129364},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.41718918085098267},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.41569802165031433}],"concepts":[{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.8879892826080322},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7576048970222473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7319692373275757},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5839171409606934},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.4659024178981781},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4528660178184509},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4317152202129364},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.41718918085098267},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.41569802165031433}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13112075","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112075","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2075/pdf?version=1635910925","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:92ae760c477e48868d1b2c7d1cfae792","is_oa":true,"landing_page_url":"https://doaj.org/article/92ae760c477e48868d1b2c7d1cfae792","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 11, p 2075 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/11/2075/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13112075","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13112075","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13112075","pdf_url":"https://www.mdpi.com/2073-8994/13/11/2075/pdf?version=1635910925","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3210961220.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W68092451","https://openalex.org/W171110949","https://openalex.org/W1030791897","https://openalex.org/W1481641293","https://openalex.org/W1592394651","https://openalex.org/W1935966726","https://openalex.org/W1964155221","https://openalex.org/W1976789532","https://openalex.org/W1984829680","https://openalex.org/W1985048439","https://openalex.org/W1991787167","https://openalex.org/W2016464878","https://openalex.org/W2124326826","https://openalex.org/W2125591649","https://openalex.org/W2165081391","https://openalex.org/W2505714894","https://openalex.org/W2551382741","https://openalex.org/W2905857446","https://openalex.org/W3086640136","https://openalex.org/W3101022838","https://openalex.org/W3113420408","https://openalex.org/W3141549464","https://openalex.org/W3159527793","https://openalex.org/W3165002432","https://openalex.org/W3165956555","https://openalex.org/W4402922113","https://openalex.org/W4403207541","https://openalex.org/W6608815102","https://openalex.org/W6640624440","https://openalex.org/W6644411035","https://openalex.org/W6678468281","https://openalex.org/W6794744604","https://openalex.org/W6872750280","https://openalex.org/W6872873400"],"related_works":["https://openalex.org/W2402582552","https://openalex.org/W2051848833","https://openalex.org/W2896350964","https://openalex.org/W1565422586","https://openalex.org/W2158039203","https://openalex.org/W2510621088","https://openalex.org/W2976558006","https://openalex.org/W4377866274","https://openalex.org/W2932511341","https://openalex.org/W2782844101"],"abstract_inverted_index":{"In":[0,70],"this":[1],"paper":[2],"we":[3,30,48,72],"introduce":[4],"and":[5,17,29],"study":[6],"a":[7,23,32,45,59],"new":[8],"generalization":[9],"of":[10,26,40,54,84],"Fibonacci":[11,56,66,78],"polynomials":[12,28,67],"which":[13,43],"generalize":[14],"Fibonacci,":[15],"Jacobsthal":[16],"Narayana":[18],"numbers,":[19],"simultaneously.":[20],"We":[21],"give":[22],"graph":[24],"interpretation":[25],"these":[27],"obtain":[31,49],"binomial":[33],"formula":[34,63],"for":[35,64,76],"them.":[36],"Moreover":[37],"by":[38,52],"modification":[39],"Pascal\u2019s":[41],"triangle,":[42],"has":[44],"symmetric":[46,82],"structure,":[47],"matrices":[50],"generated":[51],"coefficients":[53],"generalized":[55,65,77],"polynomials.":[57],"As":[58],"consequence,":[60],"the":[61,81],"direct":[62],"was":[68],"given.":[69],"addition,":[71],"determine":[73],"matrix":[74,83],"generators":[75],"polynomials,":[79],"using":[80],"initial":[85],"conditions.":[86]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
