{"id":"https://openalex.org/W7212637243","doi":"https://doi.org/10.48550/arxiv.2609.12569","title":"Rotating-Memory Fibonacci Numbers and Periodic Tilings","display_name":"Rotating-Memory Fibonacci Numbers and Periodic Tilings","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212637243","doi":"https://doi.org/10.48550/arxiv.2609.12569"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12569","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12569","pdf_url":"https://arxiv.org/pdf/2609.12569","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/2609.12569","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018007154","display_name":"Walid Abdelaidoum","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Abdelaidoum, Walid","raw_affiliation_strings":["University of Science and Technology Houari Boumediene , Faculty of Mathematics , RECITS Laboratory , P.O. Box 32 , El-Alia , 16111 Bab-Ezzouar , Algiers , Algeria;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology Houari Boumediene , Faculty of Mathematics , RECITS Laboratory , P.O. Box 32 , El-Alia , 16111 Bab-Ezzouar , Algiers , Algeria;","institution_ids":["https://openalex.org/I157169809"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066694636","display_name":"El-Mehdi Mehiri","orcid":"https://orcid.org/0000-0002-7164-3658","observed_orcids":["https://orcid.org/0000-0002-7164-3658"]},"institutions":[{"id":"https://openalex.org/I3019848993","display_name":"Mines Saint-\u00c9tienne","ror":"https://ror.org/05a1dws80","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mehiri, El-Mehdi","raw_affiliation_strings":["Mines Saint-\u00c9tienne , CMP , Department of Manufacturing Sciences and Logistics , F-13120 Gardanne , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mines Saint-\u00c9tienne , CMP , Department of Manufacturing Sciences and Logistics , F-13120 Gardanne , France","institution_ids":["https://openalex.org/I3019848993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054807235","display_name":"Hac\u00e8ne Belbachir","orcid":"https://orcid.org/0000-0001-8540-3033","observed_orcids":["https://orcid.org/0000-0001-8540-3033"]},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Belbachir, Hac\u00e8ne","raw_affiliation_strings":["University of Science and Technology Houari Boumediene , Faculty of Mathematics , RECITS Laboratory , P.O. Box 32 , El-Alia , 16111 Bab-Ezzouar , Algiers , Algeria;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology Houari Boumediene , Faculty of Mathematics , RECITS Laboratory , P.O. Box 32 , El-Alia , 16111 Bab-Ezzouar , Algiers , Algeria;","institution_ids":["https://openalex.org/I157169809"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8916000127792358,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.8916000127792358,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.09780000150203705,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.005900000222027302,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/periodic-sequences","display_name":"periodic sequences","score":0.578000009059906},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.45100000500679016},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.925000011920929},{"id":"https://openalex.org/keywords/growth-behavior","display_name":"growth behavior","score":0.49399998784065247},{"id":"https://openalex.org/keywords/restricted-compositions","display_name":"restricted compositions","score":0.8429999947547913},{"id":"https://openalex.org/keywords/bijections","display_name":"bijections","score":0.7620000243186951},{"id":"https://openalex.org/keywords/multiplicative-structure","display_name":"multiplicative structure","score":0.7260000109672546},{"id":"https://openalex.org/keywords/combinatorial-interpretation","display_name":"combinatorial interpretation","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9229999780654907},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8022000193595886},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7285000085830688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7123000025749207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6543999910354614},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.6524999737739563},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6071000099182129},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.47189998626708984},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.4413999915122986},{"id":"https://openalex.org/C21550011","wikidata":"https://www.wikidata.org/wiki/Q7632143","display_name":"Substitution tiling","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C14367171","wikidata":"https://www.wikidata.org/wiki/Q173523","display_name":"Geometric progression","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.328000009059906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32440000772476196},{"id":"https://openalex.org/C154977054","wikidata":"https://www.wikidata.org/wiki/Q1759646","display_name":"Lucas sequence","level":5,"score":0.32179999351501465},{"id":"https://openalex.org/C46581059","wikidata":"https://www.wikidata.org/wiki/Q116301","display_name":"Periodic point","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C3634175","wikidata":"https://www.wikidata.org/wiki/Q2503280","display_name":"Lucas number","level":3,"score":0.2728999853134155},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12569","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12569","pdf_url":"https://arxiv.org/pdf/2609.12569","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.2609.12569","doi":"https://doi.org/10.48550/arxiv.2609.12569","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12569","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12569","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12569","pdf_url":"https://arxiv.org/pdf/2609.12569","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/W7212637243.pdf","grobid_xml":"https://content.openalex.org/works/W7212637243.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W2009596421","https://openalex.org/W2038742312","https://openalex.org/W2119267732","https://openalex.org/W2142286671","https://openalex.org/W2313185138","https://openalex.org/W4402399544","https://openalex.org/W4402822622","https://openalex.org/W4403975908"],"related_works":["https://openalex.org/W7219734811","https://openalex.org/W4403205727","https://openalex.org/W2312582569","https://openalex.org/W7214163853","https://openalex.org/W4413400079","https://openalex.org/W7102828054","https://openalex.org/W4392302132","https://openalex.org/W4403296925","https://openalex.org/W7034247887","https://openalex.org/W2042375750"],"abstract_inverted_index":{"We":[0,44,67],"introduce":[1],"and":[2,53,57,78,128,152],"study":[3],"the":[4,13,18,25,30,36,60,85,89,93,102,114,137,142,148],"rotating-memory":[5],"Fibonacci":[6,14],"numbers,":[7],"a":[8,40,110,122,154],"periodic":[9,143],"variable-order":[10],"analogue":[11],"of":[12,20,74,88,109,121,136,157],"sequence":[15,61,104,116],"in":[16,24,72,140],"which":[17,141],"number":[19],"preceding":[21],"terms":[22,73],"used":[23],"recurrence":[26,139],"changes":[27],"cyclically":[28],"with":[29],"index.":[31],"Despite":[32],"this":[33],"varying":[34],"memory,":[35],"resulting":[37],"sequences":[38],"exhibit":[39],"remarkably":[41],"rigid":[42],"structure.":[43],"derive":[45],"closed":[46],"forms,":[47],"rational":[48],"generating":[49],"functions,":[50],"arithmetic":[51],"properties,":[52],"exact":[54],"growth":[55],"behavior,":[56],"show":[58],"that":[59],"decomposes":[62],"naturally":[63],"into":[64],"geometric":[65,134],"subsequences.":[66],"also":[68],"develop":[69],"combinatorial":[70],"interpretations":[71,135],"periodically":[75],"constrained":[76],"tilings,":[77],"restricted":[79],"compositions,":[80],"including":[81],"bijective":[82],"explanations":[83],"for":[84,161],"multiplicative":[86],"structure":[87],"sequence.":[90],"In":[91],"addition,":[92],"first":[94],"two":[95],"nonclassical":[96],"periods":[97],"admit":[98],"natural":[99],"geometry-driven":[100],"realizations:":[101],"period-2":[103],"arises":[105],"from":[106],"monomer--dimer":[107],"tilings":[108,120],"triangular":[111],"chain,":[112],"while":[113],"period-3":[115],"is":[117,145],"related":[118],"to":[119],"double":[123,129],"hexagon":[124],"strip":[125],"by":[126,147],"single":[127],"hexagons.":[130],"These":[131],"connections":[132],"provide":[133],"rotating":[138],"behavior":[144],"induced":[146],"underlying":[149],"structures":[150],"themselves,":[151],"suggest":[153],"broader":[155],"problem":[156],"constructing":[158],"analogous":[159],"models":[160],"higher":[162],"periods.":[163]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}
