{"id":"https://openalex.org/W2103646894","doi":"https://doi.org/10.37236/1523","title":"Continued Fractions and Catalan Problems","display_name":"Continued Fractions and Catalan Problems","publication_year":2000,"publication_date":"2000-07-13","ids":{"openalex":"https://openalex.org/W2103646894","doi":"https://doi.org/10.37236/1523","mag":"2103646894"},"language":"en","primary_location":{"id":"doi:10.37236/1523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r45/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r45/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039515790","display_name":"Mahendra Jani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["SS"],"is_corresponding":true,"raw_author_name":"Mahendra Jani","raw_affiliation_strings":["University"],"affiliations":[{"raw_affiliation_string":"University","institution_ids":["https://openalex.org/I4210096386"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051119625","display_name":"Robert G. Rieper","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["SS"],"is_corresponding":false,"raw_author_name":"Robert G. Rieper","raw_affiliation_strings":["University"],"affiliations":[{"raw_affiliation_string":"University","institution_ids":["https://openalex.org/I4210096386"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039515790"],"corresponding_institution_ids":["https://openalex.org/I4210096386"],"apc_list":null,"apc_paid":null,"fwci":11.9552,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.99499687,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"7","issue":"1","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":0.9923999905586243,"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":0.9923999905586243,"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/T13912","display_name":"Language, Linguistics, Cultural Analysis","score":0.9440000057220459,"subfield":{"id":"https://openalex.org/subfields/1203","display_name":"Language and Linguistics"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.9720390439033508},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.88567715883255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8455281257629395},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8313213586807251},{"id":"https://openalex.org/keywords/catalan","display_name":"Catalan","score":0.8247096538543701},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.7543792724609375},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.7520609498023987},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6057248115539551},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47411397099494934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3586077094078064},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.08643278479576111}],"concepts":[{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.9720390439033508},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.88567715883255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8455281257629395},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8313213586807251},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.8247096538543701},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.7543792724609375},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.7520609498023987},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6057248115539551},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47411397099494934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3586077094078064},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.08643278479576111},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r45/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":false,"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:10.1.1.83.821","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.821","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_7/PDF/v7i1r45.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1523","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1523","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r45/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":false,"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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2103646894.pdf","grobid_xml":"https://content.openalex.org/works/W2103646894.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1551177513","https://openalex.org/W1996878220","https://openalex.org/W2104925482","https://openalex.org/W2914659449"],"related_works":["https://openalex.org/W2404725689","https://openalex.org/W1653529408","https://openalex.org/W2951311768","https://openalex.org/W4298144150","https://openalex.org/W2331795269","https://openalex.org/W2103167772","https://openalex.org/W1493023638","https://openalex.org/W2340799374","https://openalex.org/W1968233098","https://openalex.org/W2103646894"],"abstract_inverted_index":{"We":[0],"find":[1],"a":[2,7,38,53,66],"generating":[3,33],"function":[4],"expressed":[5,36],"as":[6,37],"continued":[8,39],"fraction":[9],"that":[10,51],"enumerates":[11],"ordered":[12],"trees":[13],"by":[14],"the":[15,45,74],"number":[16,55],"of":[17,47,56,59,68],"vertices":[18],"at":[19],"different":[20],"levels.":[21],"Several":[22],"Catalan":[23],"problems":[24,43],"are":[25],"mapped":[26],"to":[27],"an":[28],"ordered-tree":[29],"problem":[30],"and":[31,64,71],"their":[32],"functions":[34],"also":[35],"fraction.":[40],"Among":[41],"these":[42],"is":[44],"enumeration":[46],"$(132)$-pattern":[48],"avoiding":[49],"permutations":[50],"have":[52],"given":[54],"increasing":[57],"patterns":[58],"length":[60],"$k$.":[61],"This":[62],"extends":[63],"illuminates":[65],"result":[67],"Robertson,":[69],"Wilf":[70],"Zeilberger":[72],"for":[73],"case":[75],"$k=3$.":[76]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
