{"id":"https://openalex.org/W1554222672","doi":"https://doi.org/10.37236/1052","title":"Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes","display_name":"Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes","publication_year":2006,"publication_date":"2006-03-21","ids":{"openalex":"https://openalex.org/W1554222672","doi":"https://doi.org/10.37236/1052","mag":"1554222672"},"language":"en","primary_location":{"id":"doi:10.37236/1052","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1052","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r26/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109206727","display_name":"Brad Jackson","orcid":null},"institutions":[{"id":"https://openalex.org/I51504820","display_name":"San Jose State University","ror":"https://ror.org/04qyvz380","country_code":"US","type":"education","lineage":["https://openalex.org/I51504820"]},{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"Brad Jackson","raw_affiliation_strings":["Dept. of Computer Science University of Victoria, CANADA","Dept. of Mathematics San Jose State University, USA"],"affiliations":[{"raw_affiliation_string":"Dept. of Computer Science University of Victoria, CANADA","institution_ids":["https://openalex.org/I212119943"]},{"raw_affiliation_string":"Dept. of Mathematics San Jose State University, USA","institution_ids":["https://openalex.org/I51504820"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048017151","display_name":"Frank Ruskey","orcid":"https://orcid.org/0000-0001-5523-7185"},"institutions":[{"id":"https://openalex.org/I212119943","display_name":"University of Victoria","ror":"https://ror.org/04s5mat29","country_code":"CA","type":"education","lineage":["https://openalex.org/I212119943"]},{"id":"https://openalex.org/I51504820","display_name":"San Jose State University","ror":"https://ror.org/04qyvz380","country_code":"US","type":"education","lineage":["https://openalex.org/I51504820"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Frank Ruskey","raw_affiliation_strings":["Dept. of Mathematics San Jose State University, USA","Dept. of Computer Science University of Victoria, CANADA"],"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics San Jose State University, USA","institution_ids":["https://openalex.org/I51504820"]},{"raw_affiliation_string":"Dept. of Computer Science University of Victoria, CANADA","institution_ids":["https://openalex.org/I212119943"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109206727"],"corresponding_institution_ids":["https://openalex.org/I212119943","https://openalex.org/I51504820"],"apc_list":null,"apc_paid":null,"fwci":2.3592,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.87645368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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-number","display_name":"Fibonacci number","score":0.9322117567062378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8406708240509033},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7882099151611328},{"id":"https://openalex.org/keywords/integer-sequence","display_name":"Integer sequence","score":0.7838019132614136},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6763947010040283},{"id":"https://openalex.org/keywords/pisano-period","display_name":"Pisano period","score":0.5912877321243286},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5798967480659485},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5199357867240906},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5190063714981079},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.5037488341331482},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.16734036803245544},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1617947220802307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07601794600486755}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9322117567062378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8406708240509033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7882099151611328},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.7838019132614136},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6763947010040283},{"id":"https://openalex.org/C174757984","wikidata":"https://www.wikidata.org/wiki/Q4351325","display_name":"Pisano period","level":5,"score":0.5912877321243286},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5798967480659485},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5199357867240906},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5190063714981079},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.5037488341331482},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.16734036803245544},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1617947220802307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07601794600486755},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1052","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1052","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.123.7233","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.7233","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uvic.ca/~ruskey/Publications/MetaFib/MetaFib.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.67.7922","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.7922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csr.uvic.ca/~fruskey/Publications/MetaFib/MetaFib.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.4281","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.4281","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r26.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1052","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1052","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r26/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1554222672.pdf","grobid_xml":"https://content.openalex.org/works/W1554222672.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W169615456","https://openalex.org/W1578978375","https://openalex.org/W1991912396","https://openalex.org/W1993449345","https://openalex.org/W2035787671","https://openalex.org/W2083368438","https://openalex.org/W2752853835","https://openalex.org/W2752908210"],"related_works":["https://openalex.org/W2964139039","https://openalex.org/W2002698978","https://openalex.org/W2164636225","https://openalex.org/W2064332477","https://openalex.org/W4292230397","https://openalex.org/W2349059505","https://openalex.org/W1597235206","https://openalex.org/W2354266039","https://openalex.org/W3167133355","https://openalex.org/W4308022429"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2],"family":[3,37],"of":[4,13,23,28,38,44,59,69],"meta-Fibonacci":[5,39],"sequences":[6,22,40,46,60,64],"which":[7],"arise":[8],"in":[9,19,56,65],"studying":[10],"the":[11,16,66],"number":[12],"leaves":[14],"at":[15],"largest":[17],"level":[18],"certain":[20],"infinite":[21],"binary":[24,32],"trees,":[25],"restricted":[26],"compositions":[27],"an":[29],"integer,":[30],"and":[31,41,52],"compact":[33],"codes.":[34],"For":[35],"this":[36],"two":[42],"families":[43,58],"related":[45],"we":[47],"derive":[48],"ordinary":[49],"generating":[50],"functions":[51],"recurrence":[53],"relations.":[54],"Included":[55],"these":[57],"are":[61],"several":[62],"well-known":[63],"Online":[67],"Encyclopedia":[68],"Integer":[70],"Sequences":[71],"(OEIS).":[72]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
