{"id":"https://openalex.org/W7220954792","doi":"https://doi.org/10.48550/arxiv.2610.07901","title":"Higher-dimensional Golden Section, Generalized Fibonacci Sequence, and Multiple Online Leasing","display_name":"Higher-dimensional Golden Section, Generalized Fibonacci Sequence, and Multiple Online Leasing","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220954792","doi":"https://doi.org/10.48550/arxiv.2610.07901"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07901","pdf_url":"https://arxiv.org/pdf/2610.07901","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":"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/2610.07901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157923804","display_name":"Hu Maolin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Maolin, Hu","raw_affiliation_strings":["School of Mathematics and Statistics , Huaiyin Normal University , Huaian , Jiangsu , 223300 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Huaiyin Normal University , Huaian , Jiangsu , 223300 , China","institution_ids":["https://openalex.org/I4210147117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157986956","display_name":"Luo Chu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4396570619","display_name":"Great Bay University","ror":"https://ror.org/01hdgge16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4396570619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chu, Luo","raw_affiliation_strings":["Great Bay University , Dongguan , Guangdong , 523000 , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Great Bay University , Dongguan , Guangdong , 523000 , China;","institution_ids":["https://openalex.org/I4396570619"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137964182","display_name":"Weidong Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weidong, Xu","raw_affiliation_strings":["School of Management , Zhejiang University , Hangzhou 310058 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management , Zhejiang University , Hangzhou 310058 , China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.5419999957084656,"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":0.5419999957084656,"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/T12288","display_name":"Optimization and Search Problems","score":0.4165000021457672,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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":0.004699999932199717,"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/golden-ratio","display_name":"golden ratio","score":0.9369999766349792},{"id":"https://openalex.org/keywords/generalized-fibonacci-sequences","display_name":"generalized Fibonacci sequences","score":0.8360000252723694},{"id":"https://openalex.org/keywords/ski-rental-problem","display_name":"ski rental problem","score":0.906000018119812},{"id":"https://openalex.org/keywords/competitive-ratio","display_name":"competitive ratio","score":0.8019999861717224},{"id":"https://openalex.org/keywords/fibonacci-matrix","display_name":"Fibonacci matrix","score":0.9139999747276306},{"id":"https://openalex.org/keywords/determinant-formula","display_name":"determinant formula","score":0.6669999957084656},{"id":"https://openalex.org/keywords/continuous-relaxation","display_name":"continuous relaxation","score":0.7409999966621399}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9634000062942505},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.9309999942779541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5843999981880188},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.37549999356269836},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3716000020503998},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.3481000065803528},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3353999853134155},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3294000029563904},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.319599986076355},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29580000042915344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2935999929904938},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.2718999981880188}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07901","pdf_url":"https://arxiv.org/pdf/2610.07901","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.07901","doi":"https://doi.org/10.48550/arxiv.2610.07901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07901","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:2610.07901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07901","pdf_url":"https://arxiv.org/pdf/2610.07901","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":"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/W7220954792.pdf","grobid_xml":"https://content.openalex.org/works/W7220954792.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4402633812","https://openalex.org/W4403207782","https://openalex.org/W4402911796","https://openalex.org/W2513604696","https://openalex.org/W4402831227","https://openalex.org/W4403297320","https://openalex.org/W2155593484","https://openalex.org/W2237038744","https://openalex.org/W3013051220","https://openalex.org/W7118226344"],"abstract_inverted_index":{"We":[0,98,130,175,190,220,236],"discover":[1],"a":[2,121,147,177,216],"connection":[3],"between":[4],"the":[5,10,15,24,34,47,53,72,92,102,116,138,151,192,197,228,232,238,244],"classical":[6],"golden":[7,35,65,73,81,200],"section":[8,36,201],"and":[9,44,67,78,84,106,110,137,179,182],"online":[11,69,163,168],"leasing":[12,169],"problem:":[13],"when":[14],"number":[16],"of":[17,57,170,173],"skis":[18],"increases":[19],"from":[20],"one":[21,42],"to":[22,29,120,226,242],"two,":[23],"optimal":[25,54,186,193,229],"competitive":[26,55,188],"algorithm":[27],"is":[28,185,195],"rent":[30],"two":[31,88],"pairs":[32,172],"until":[33],"point$(\\sqrt{5}-1)s/2$":[37],"within":[38],"[0,s],":[39],"then":[40],"buy":[41,46],"pair,":[43],"finally":[45],"second":[48],"at":[49],"time":[50],"$s$,":[51],"achieving":[52,246],"ratio":[56,104],"$(5+\\sqrt{5})/4$.":[58],"Building":[59],"on":[60,87],"this,":[61],"we":[62,75,126,165,214],"explore":[63,221],"higher-dimensional":[64,80],"sections":[66],"multiple":[68,167],"leasing.":[70],"For":[71,162],"section,":[74],"define":[76],"geometric-type":[77,103],"harmonic-type":[79,107,199],"sections,":[82],"$\u03c4^{(m)}$":[83],"$T^{(m)}$,":[85],"based":[86],"equivalent":[89],"propositions":[90],"dividing":[91],"unit":[93],"segment":[94],"into":[95],"$m$":[96,171],"segments.":[97],"establish":[99,127],"equations":[100],"for":[101,209],"$\u03bb$":[105],"basis":[108],"$\u03c9$,":[109],"investigate":[111],"their":[112,128],"algebraic":[113],"characteristics.":[114],"Extending":[115],"$k$-generalized":[117],"Fibonacci":[118,124,139,152,160],"sequence":[119],"bi-infinite":[122],"$m$-generalized":[123],"sequence,":[125],"relationship.":[129],"introduce":[131],"novel":[132],"concepts":[133],"including":[134],"generating":[135],"sequences":[136],"matrix,":[140],"investigating":[141],"its":[142,155,223],"submatrices.":[143],"Results":[144],"such":[145],"as":[146],"determinant":[148],"formula":[149],"involving":[150],"matrix":[153],"demonstrate":[154],"effectiveness":[156],"in":[157],"studying":[158],"generalized":[159],"sequences.":[161],"leasing,":[164],"consider":[166],"skis.":[174],"design":[176],"control":[178],"balancing":[180],"strategy":[181,194],"prove":[183],"it":[184],"via":[187],"analysis.":[189,251],"show":[191],"precisely":[196],"$m$-dimensional":[198],"method.":[202],"Since":[203],"explicit":[204],"solutions":[205],"may":[206],"not":[207],"exist":[208],"dimensions":[210],"higher":[211],"than":[212],"four,":[213],"propose":[215,237],"continuous":[217],"relaxation":[218],"problem.":[219],"using":[222],"relaxed":[224],"solution":[225,230],"approximate":[227],"or":[231],"largest":[233],"real":[234],"root.":[235],"mantissa":[239],"weighting":[240],"method":[241],"solve":[243],"equation,":[245],"high":[247],"accuracy":[248],"through":[249],"error":[250]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}