{"id":"https://openalex.org/W4410621160","doi":"https://doi.org/10.1016/j.aam.2025.102911","title":"q-Super Catalan numbers: Combinatorial identities, generating functions, and Narayana refinements","display_name":"q-Super Catalan numbers: Combinatorial identities, generating functions, and Narayana refinements","publication_year":2025,"publication_date":"2025-05-23","ids":{"openalex":"https://openalex.org/W4410621160","doi":"https://doi.org/10.1016/j.aam.2025.102911"},"language":"en","primary_location":{"id":"doi:10.1016/j.aam.2025.102911","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102911","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.aam.2025.102911","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117644643","display_name":"Arthur Rodelet\u2013Causse","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arthur Rodelet\u2013Causse","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063422166","display_name":"Lenny Tevlin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lenny Tevlin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5117644643"],"corresponding_institution_ids":[],"apc_list":{"value":2670,"currency":"USD","value_usd":2670},"apc_paid":{"value":2670,"currency":"USD","value_usd":2670},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16675518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"169","issue":null,"first_page":"102911","last_page":"102911"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994000196456909,"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":0.9775000214576721,"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":0.9164561033248901},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.8799759745597839},{"id":"https://openalex.org/keywords/catalan","display_name":"Catalan","score":0.781171441078186},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5185102224349976},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49333301186561584},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36116254329681396},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27266165614128113},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.15301766991615295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9164561033248901},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.8799759745597839},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.781171441078186},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5185102224349976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49333301186561584},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36116254329681396},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27266165614128113},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.15301766991615295},{"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:10.1016/j.aam.2025.102911","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102911","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2505.09821","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.09821","pdf_url":"https://arxiv.org/pdf/2505.09821","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"doi:10.1016/j.aam.2025.102911","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.aam.2025.102911","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W650710040","https://openalex.org/W1972006298","https://openalex.org/W1980377053","https://openalex.org/W1991394102","https://openalex.org/W2008052995","https://openalex.org/W2020518828","https://openalex.org/W2021347618","https://openalex.org/W2028684258","https://openalex.org/W2059459845","https://openalex.org/W2099953837","https://openalex.org/W2107406456","https://openalex.org/W2134984950","https://openalex.org/W2145536234","https://openalex.org/W2148578787","https://openalex.org/W3137271103","https://openalex.org/W4229879642","https://openalex.org/W4295292729","https://openalex.org/W4388419266","https://openalex.org/W6607391288","https://openalex.org/W6621598650","https://openalex.org/W6652495812","https://openalex.org/W6681294115","https://openalex.org/W6691066985","https://openalex.org/W6741055480"],"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/W2412261190","https://openalex.org/W2103167772","https://openalex.org/W2953909559","https://openalex.org/W1493023638","https://openalex.org/W2340799374"],"abstract_inverted_index":{"We":[0,66],"derive":[1,48],"a":[2,49,77,81],"number":[3],"of":[4,19,61,72,89,113],"combinatorial":[5,22,78],"identities":[6,23,40,108,112],"satisfied":[7],"by":[8],"the":[9,20,29,62,69,85],"q":[10,30,38,53,97,101,135],"-super":[11,31],"Catalan":[12,32,64],"numbers.":[13,33,55,65],"In":[14],"particular,":[15],"we":[16,35,57,93,125],"extend":[17],"some":[18,37,107],"known":[21],"(Touchard,":[24],"Koshy,":[25],"Reed":[26],"Dawson)":[27],"to":[28],"Next,":[34],"introduce":[36,58,94],"-convolution":[39],"involving":[41],"q-central":[42],"binomial":[43],"and":[44,47,75,105,116],"q-Catalan":[45],"numbers,":[46],"generating":[50],"function":[51],"for":[52],"-Catalan":[54],"Then":[56,92],"Narayana-type":[59],"refinements":[60,74,129],"super":[63],"prove":[67,99,106,126],"algebraically":[68],"\u03b3":[70,103],"-positivity":[71],"those":[73],"give":[76],"proof":[79],"in":[80,134],"special":[82],"case":[83],"through":[84],"type":[86],"B":[87],"analog":[88],"noncrossing":[90],"partitions.":[91],"their":[95,100],"natural":[96],"-analogs,":[98],"-":[102],"-positivity,":[104],"they":[109],"satisfy,":[110],"generalizing":[111],"Kreweras":[114],"[17]":[115],"Le":[117],"Jen-Shoo":[118],"[11]":[119],".":[120,136],"Using":[121],"yet":[122],"another":[123],"identity,":[124],"that":[127],"these":[128],"are":[130],"positive":[131],"integer":[132],"polynomials":[133]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-05-23T00:00:00"}
