{"id":"https://openalex.org/W2964227275","doi":"https://doi.org/10.1016/j.aam.2019.01.009","title":"(q,t)-Catalan numbers: gamma expansions, pattern avoidances, and the (\u22121)-phenomenon","display_name":"(q,t)-Catalan numbers: gamma expansions, pattern avoidances, and the (\u22121)-phenomenon","publication_year":2019,"publication_date":"2019-02-18","ids":{"openalex":"https://openalex.org/W2964227275","doi":"https://doi.org/10.1016/j.aam.2019.01.009","mag":"2964227275"},"language":"en","primary_location":{"id":"doi:10.1016/j.aam.2019.01.009","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aam.2019.01.009","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010700631","display_name":"Shishuo Fu","orcid":"https://orcid.org/0000-0002-4052-3223"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shishuo Fu","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Huxi campus LD506, Chongqing 401331, PR China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Huxi campus LD506, Chongqing 401331, PR China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025724291","display_name":"Dazhao Tang","orcid":"https://orcid.org/0000-0003-3281-6912"},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dazhao Tang","raw_affiliation_strings":["College of Mathematics and Statistics, Chongqing University, Huxi campus LD506, Chongqing 401331, PR China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Chongqing University, Huxi campus LD506, Chongqing 401331, PR China","institution_ids":["https://openalex.org/I158842170"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072394907","display_name":"Bin Han","orcid":"https://orcid.org/0000-0001-7124-2056"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bin Han","raw_affiliation_strings":["Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108363298","display_name":"Jiang Zeng","orcid":"https://orcid.org/0000-0002-7063-1882"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jiang Zeng","raw_affiliation_strings":["Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025724291"],"corresponding_institution_ids":["https://openalex.org/I158842170"],"apc_list":{"value":2670,"currency":"USD","value_usd":2670},"apc_paid":null,"fwci":2.0309,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85566343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"106","issue":null,"first_page":"57","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9779999852180481,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8315494060516357},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.8131039142608643},{"id":"https://openalex.org/keywords/phenomenon","display_name":"Phenomenon","score":0.8093643188476562},{"id":"https://openalex.org/keywords/catalan","display_name":"Catalan","score":0.7702044248580933},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.6719103455543518},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5905776619911194},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.5028120875358582},{"id":"https://openalex.org/keywords/derangement","display_name":"Derangement","score":0.4507543742656708},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4235232174396515},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34301477670669556},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.07648226618766785},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06419900059700012},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.057236820459365845},{"id":"https://openalex.org/keywords/evolutionary-biology","display_name":"Evolutionary biology","score":0.045406848192214966}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8315494060516357},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.8131039142608643},{"id":"https://openalex.org/C50335755","wikidata":"https://www.wikidata.org/wiki/Q483247","display_name":"Phenomenon","level":2,"score":0.8093643188476562},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.7702044248580933},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.6719103455543518},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5905776619911194},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5028120875358582},{"id":"https://openalex.org/C38298161","wikidata":"https://www.wikidata.org/wiki/Q1207920","display_name":"Derangement","level":2,"score":0.4507543742656708},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4235232174396515},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34301477670669556},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.07648226618766785},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06419900059700012},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.057236820459365845},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.045406848192214966},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.aam.2019.01.009","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aam.2019.01.009","pdf_url":null,"source":{"id":"https://openalex.org/S164906323","display_name":"Advances in Applied Mathematics","issn_l":"0196-8858","issn":["0196-8858","1090-2074"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02075053v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02075053","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Applied Mathematics, 2019, 106, pp.57-95. ⟨10.1016/j.aam.2019.01.009⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G659475532","display_name":null,"funder_award_id":"2018CDXYST0024","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8881670054","display_name":null,"funder_award_id":"11501061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W166539567","https://openalex.org/W186403072","https://openalex.org/W1485834153","https://openalex.org/W1540289938","https://openalex.org/W1548412882","https://openalex.org/W1562346447","https://openalex.org/W1601893025","https://openalex.org/W1704867954","https://openalex.org/W1769272574","https://openalex.org/W1864009735","https://openalex.org/W1971490887","https://openalex.org/W1988430587","https://openalex.org/W1991394102","https://openalex.org/W1995198773","https://openalex.org/W2004076922","https://openalex.org/W2011262620","https://openalex.org/W2013327405","https://openalex.org/W2014724230","https://openalex.org/W2017072639","https://openalex.org/W2022892305","https://openalex.org/W2023142381","https://openalex.org/W2039253374","https://openalex.org/W2043605821","https://openalex.org/W2064421824","https://openalex.org/W2071829066","https://openalex.org/W2072036387","https://openalex.org/W2072875206","https://openalex.org/W2075853453","https://openalex.org/W2121119116","https://openalex.org/W2122111034","https://openalex.org/W2144105674","https://openalex.org/W2165384925","https://openalex.org/W2167681819","https://openalex.org/W2340541605","https://openalex.org/W2489414373","https://openalex.org/W2583084574","https://openalex.org/W2598315094","https://openalex.org/W2769849871","https://openalex.org/W2810586570","https://openalex.org/W2950783846","https://openalex.org/W2951595946","https://openalex.org/W2963532774","https://openalex.org/W4297782679","https://openalex.org/W6632998992","https://openalex.org/W6746172606","https://openalex.org/W6764262565"],"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":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}