{"id":"https://openalex.org/W3000617093","doi":"https://doi.org/10.37236/1745","title":"Self-Describing Sequences and the Catalan Family Tree","display_name":"Self-Describing Sequences and the Catalan Family Tree","publication_year":2003,"publication_date":"2003-05-29","ids":{"openalex":"https://openalex.org/W3000617093","doi":"https://doi.org/10.37236/1745","mag":"3000617093"},"language":"en","primary_location":{"id":"doi:10.37236/1745","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1745","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1n5/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/v10i1n5/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108684609","display_name":"Zoran \u0160uni\u1e31","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zoran \u0160uni\u0199","raw_affiliation_strings":["Department of Mathematics Texas A&M University College Station, TX 77843-3368, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Texas A&M University College Station, TX 77843-3368, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108684609"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":0.3546,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.65840807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","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":0.9984999895095825,"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":0.9984999895095825,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9968000054359436,"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":0.992900013923645,"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/catalan-number","display_name":"Catalan number","score":0.9692919254302979},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8743122816085815},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7518179416656494},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6609996557235718},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6475788354873657},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6385003328323364},{"id":"https://openalex.org/keywords/integer-sequence","display_name":"Integer sequence","score":0.6248429417610168},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6199073195457458},{"id":"https://openalex.org/keywords/catalan","display_name":"Catalan","score":0.6172747611999512},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5965921878814697},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4785209894180298},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.1692686676979065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09399396181106567}],"concepts":[{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.9692919254302979},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8743122816085815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7518179416656494},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6609996557235718},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6475788354873657},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6385003328323364},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.6248429417610168},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6199073195457458},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.6172747611999512},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5965921878814697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4785209894180298},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.1692686676979065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09399396181106567},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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":1,"locations":[{"id":"doi:10.37236/1745","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1745","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1n5/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"}],"best_oa_location":{"id":"doi:10.37236/1745","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1745","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1n5/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000617093.pdf","grobid_xml":"https://content.openalex.org/works/W3000617093.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W15048363","https://openalex.org/W1551177513","https://openalex.org/W2062984219","https://openalex.org/W2148330971","https://openalex.org/W3155769461"],"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/W2412261190","https://openalex.org/W1493023638","https://openalex.org/W1968233098","https://openalex.org/W4231117739"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,75,79],"transformation":[3,16],"of":[4,21,50],"finite":[5],"integer":[6],"sequences,":[7],"show":[8],"that":[9,18,32,38,53],"every":[10,42],"sequence":[11],"eventually":[12],"stabilizes":[13],"under":[14],"this":[15],"and":[17],"the":[19,27,48],"number":[20,49],"fixed":[22,34],"points":[23],"is":[24,45],"counted":[25],"by":[26,71],"Catalan":[28,76],"numbers.":[29],"The":[30],"sequences":[31,70],"are":[33,35,54],"precisely":[36],"those":[37],"describe":[39],"themselves":[40],"\u2014":[41],"term":[43],"$t$":[44],"equal":[46],"to":[47,65],"previous":[51],"terms":[52],"smaller":[55],"than":[56],"$t$.":[57],"In":[58],"addition,":[59],"we":[60],"provide":[61],"an":[62],"easy":[63],"way":[64],"enumerate":[66],"all":[67],"these":[68],"self-describing":[69],"organizing":[72],"them":[73],"in":[74],"tree":[77],"with":[78],"specific":[80],"labelling":[81],"system.":[82]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}