{"id":"https://openalex.org/W7213233157","doi":"https://doi.org/10.48550/arxiv.2609.14386","title":"The (p,q)-Analogues of Bi-Stirling Eulerian Polynomials via continued fractions","display_name":"The (p,q)-Analogues of Bi-Stirling Eulerian Polynomials via continued fractions","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213233157","doi":"https://doi.org/10.48550/arxiv.2609.14386"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14386","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14386","pdf_url":"https://arxiv.org/pdf/2609.14386","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151777337","display_name":"Chao Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Lyon 1 Universit\u00e9","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/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Xu, Chao","raw_affiliation_strings":["Universit\u00e9 Claude Bernard Lyon 1 , CNRS UMR 5208 , Institut Camille Jordan , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Claude Bernard Lyon 1 , CNRS UMR 5208 , Institut Camille Jordan , France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I4210104796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108363298","display_name":"Jiang Zeng","orcid":"https://orcid.org/0000-0002-7063-1882","observed_orcids":["https://orcid.org/0000-0002-7063-1882"]},"institutions":[{"id":"https://openalex.org/I146620803","display_name":"Wenzhou University","ror":"https://ror.org/020hxh324","country_code":"CN","type":"education","lineage":["https://openalex.org/I146620803"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeng, Jiang","raw_affiliation_strings":["College of Mathematics and Physics , Wenzhou University , Wenzhou 325035 , China ;,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics , Wenzhou University , Wenzhou 325035 , China ;,","institution_ids":["https://openalex.org/I146620803"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":1.0,"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":1.0,"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":0.0,"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":0.0,"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/permutation-statistics","display_name":"permutation statistics","score":0.7680000066757202},{"id":"https://openalex.org/keywords/descent","display_name":"descent","score":0.8169999718666077},{"id":"https://openalex.org/keywords/excedances","display_name":"excedances","score":0.9990000128746033},{"id":"https://openalex.org/keywords/total-positivity","display_name":"total positivity","score":0.9890000224113464},{"id":"https://openalex.org/keywords/gamma-positivity","display_name":"gamma-positivity","score":0.8999999761581421},{"id":"https://openalex.org/keywords/eulerian-polynomials","display_name":"Eulerian polynomials","score":0.6570000052452087}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.920199990272522},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.8723000288009644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8418999910354614},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7364000082015991},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5898000001907349},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5390999913215637},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4205999970436096},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.414000004529953},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.3749000132083893},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C64137656","wikidata":"https://www.wikidata.org/wiki/Q1064405","display_name":"Parity of a permutation","level":4,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14386","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14386","pdf_url":"https://arxiv.org/pdf/2609.14386","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},{"id":"doi:10.48550/arxiv.2609.14386","doi":"https://doi.org/10.48550/arxiv.2609.14386","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14386","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14386","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14386","pdf_url":"https://arxiv.org/pdf/2609.14386","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8615355325","display_name":null,"funder_award_id":"202206220034","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213233157.pdf","grobid_xml":"https://content.openalex.org/works/W7213233157.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1525032898"],"related_works":["https://openalex.org/W7208796287","https://openalex.org/W7207709556","https://openalex.org/W2011262620","https://openalex.org/W4400409242","https://openalex.org/W4404168315","https://openalex.org/W4402402066","https://openalex.org/W3216574486","https://openalex.org/W1509462017","https://openalex.org/W4411721685","https://openalex.org/W2039253374"],"abstract_inverted_index":{"We":[0],"establish":[1],"Jacobi-type":[2],"continued":[3],"fraction":[4],"expansions":[5],"for":[6,74],"(p,q)-analogues":[7],"of":[8,27,56,59,77,87],"the":[9,57,91],"bi-Stirling":[10],"Eulerian":[11,16],"polynomials,":[12],"which":[13],"refine":[14],"classical":[15],"statistics":[17],"on":[18,48,69],"permutations.":[19],"These":[20],"polynomials":[21],"admit":[22],"equivalent":[23],"definitions":[24],"in":[25,90],"terms":[26],"descents":[28],"or":[29],"excedances.":[30],"The":[31],"parameters":[32],"p":[33],"and":[34,42,61,72,83],"q":[35],"encode":[36],"refined":[37],"permutation":[38],"statistics,":[39],"including":[40],"(ldes,rasc)":[41],"(cros,nest).":[43],"Our":[44,80],"approach":[45],"is":[46],"based":[47],"weighted":[49],"Motzkin":[50],"path":[51],"models":[52],"arising":[53],"from":[54],"variants":[55],"bijections":[58],"Fran\u00e7on--Viennot":[60],"Foata--Zeilberger.":[62],"As":[63],"applications,":[64],"we":[65],"obtain":[66],"new":[67],"results":[68,81],"total":[70],"positivity":[71],"gamma-positivity":[73],"several":[75],"families":[76],"enumerative":[78],"polynomials.":[79],"unify":[82],"extend":[84],"a":[85],"number":[86],"recent":[88],"works":[89],"literature.":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}