{"id":"https://openalex.org/W7204952227","doi":"https://doi.org/10.48550/arxiv.2608.28782","title":"Stable Solutions to Generalizations of Fibonacci Relations of Higher Order","display_name":"Stable Solutions to Generalizations of Fibonacci Relations of Higher Order","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204952227","doi":"https://doi.org/10.48550/arxiv.2608.28782"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28782","pdf_url":"https://arxiv.org/pdf/2608.28782","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062803323","display_name":"Timmy Ma","orcid":"https://orcid.org/0009-0003-8122-9455","observed_orcids":["https://orcid.org/0009-0003-8122-9455"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ma, Timmy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148917056","display_name":"Richard Vernon","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vernon, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9531000256538391,"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":0.9531000256538391,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.02280000038444996,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.009600000455975533,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-fibonacci-sequences","display_name":"generalized Fibonacci sequences","score":0.9729999899864197},{"id":"https://openalex.org/keywords/initial-values","display_name":"initial values","score":0.6650000214576721},{"id":"https://openalex.org/keywords/linear-recurrence-relations","display_name":"linear difference equations","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7883999943733215},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7397000193595886},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6915000081062317},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5669000148773193},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5392000079154968},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43720000982284546},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3815999925136566},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.3695000112056732},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3495999872684479},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28782","pdf_url":"https://arxiv.org/pdf/2608.28782","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.28782","doi":"https://doi.org/10.48550/arxiv.2608.28782","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28782","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.28782","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28782","pdf_url":"https://arxiv.org/pdf/2608.28782","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204952227.pdf","grobid_xml":"https://content.openalex.org/works/W7204952227.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W70678348","https://openalex.org/W4416354915","https://openalex.org/W3176617461","https://openalex.org/W4407648256","https://openalex.org/W6922466811","https://openalex.org/W4416350485","https://openalex.org/W2045499580","https://openalex.org/W2183895130","https://openalex.org/W2908697971","https://openalex.org/W1587339471"],"abstract_inverted_index":{"We":[0,20,30],"reformulate":[1],"and":[2],"discuss":[3],"the":[4,7,26],"conditions":[5],"for":[6],"initial":[8],"values":[9],"in":[10],"which":[11],"a":[12,33],"generalized":[13,27,42],"Fibonacci":[14],"sequence":[15,44],"is":[16],"eventually":[17,39],"strictly":[18,40],"monotonic.":[19],"then":[21],"extend":[22],"this":[23],"exploration":[24],"to":[25],"\\(k\\)-bonacci":[28,43],"sequence.":[29],"also":[31],"give":[32],"lower":[34],"bound":[35],"on":[36],"when":[37],"an":[38],"monotone":[41],"becomes":[45],"monotone.":[46]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-02T00:00:00"}
