{"id":"https://openalex.org/W7223203774","doi":"https://doi.org/10.48550/arxiv.2610.28691","title":"Two q-Deformations of Narayana Polynomials: Rogers Moments, Hankel Positivity, and q-Narayana Kernels","display_name":"Two q-Deformations of Narayana Polynomials: Rogers Moments, Hankel Positivity, and q-Narayana Kernels","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223203774","doi":"https://doi.org/10.48550/arxiv.2610.28691"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28691","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28691","pdf_url":"https://arxiv.org/pdf/2610.28691","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/2610.28691","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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/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/I146620803","display_name":"Wenzhou University","ror":"https://ror.org/020hxh324","country_code":"CN","type":"education","lineage":["https://openalex.org/I146620803"]},{"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":["CN","FR"],"is_corresponding":true,"raw_author_name":"Zeng, Jiang","raw_affiliation_strings":["College of Mathematics and Physics , Wenzhou University , Wenzhou 325035 , China","Universit\u00e9 Claude Bernard Lyon 1 , CNRS UMR 5208 , Institut Camille Jordan , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Physics , Wenzhou University , Wenzhou 325035 , China","institution_ids":["https://openalex.org/I146620803"]},{"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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108363298"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I146620803","https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9926999807357788,"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":0.9926999807357788,"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":0.0032999999821186066,"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":0.003100000089034438,"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/narayana-polynomials","display_name":"Narayana polynomials","score":0.906000018119812},{"id":"https://openalex.org/keywords/q-deformation","display_name":"q-deformation","score":0.9210000038146973},{"id":"https://openalex.org/keywords/total-positivity","display_name":"total positivity","score":0.9150000214576721},{"id":"https://openalex.org/keywords/change-of-basis","display_name":"change of basis","score":0.6909999847412109}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8938000202178955},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6668000221252441},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6243000030517578},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5968000292778015},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5029000043869019},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.4699999988079071},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41769999265670776},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4146000146865845},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.3741999864578247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3693999946117401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36469998955726624},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32820001244544983},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2531999945640564},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28691","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28691","pdf_url":"https://arxiv.org/pdf/2610.28691","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.2610.28691","doi":"https://doi.org/10.48550/arxiv.2610.28691","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28691","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:2610.28691","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28691","pdf_url":"https://arxiv.org/pdf/2610.28691","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223203774.pdf","grobid_xml":"https://content.openalex.org/works/W7223203774.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1983009349","https://openalex.org/W2073320441","https://openalex.org/W2592315004","https://openalex.org/W2804179010","https://openalex.org/W2850332003","https://openalex.org/W2964045128","https://openalex.org/W3035395790","https://openalex.org/W3134498533","https://openalex.org/W4210351713","https://openalex.org/W4389984287","https://openalex.org/W4394952213","https://openalex.org/W4396605149","https://openalex.org/W4410621160","https://openalex.org/W4417449742","https://openalex.org/W7125154053","https://openalex.org/W7166045327","https://openalex.org/W7167227897","https://openalex.org/W7167276206","https://openalex.org/W7204165078","https://openalex.org/W7214725787"],"related_works":["https://openalex.org/W2592315004","https://openalex.org/W7133947964","https://openalex.org/W7167276206","https://openalex.org/W2107406456","https://openalex.org/W2057367819","https://openalex.org/W2903155050","https://openalex.org/W2021347618","https://openalex.org/W4210351713","https://openalex.org/W2550284455","https://openalex.org/W2023794705"],"abstract_inverted_index":{"We":[0,81],"study":[1],"two":[2,91,104],"$q$-deformations":[3],"of":[4,28,31,41,54,68,100],"the":[5,20,42,93,103],"continuous":[6,21],"interpolation":[7],"between":[8],"type":[9,13,72,75],"$B$":[10,76],"and":[11,50,74,79,106],"shifted":[12],"$A$":[14,73],"Narayana":[15,77],"polynomials,":[16],"both":[17],"constructed":[18],"from":[19],"$q$-ultraspherical":[22],"(Rogers)":[23],"functional.":[24],"The":[25],"first":[26],"consists":[27],"affine":[29],"moments":[30],"ordinary":[32],"powers.":[33],"For":[34],"fixed":[35],"$0-1$,":[36],"we":[37],"prove":[38],"total":[39,52,85],"positivity":[40,53],"kernel":[43],"triangle":[44],"by":[45,58],"a":[46,59,65],"Jackson":[47],"$q$-Bessel--Edrei":[48],"factorization":[49],"strict":[51],"its":[55],"associated":[56],"square":[57],"discrete":[60],"moment":[61],"representation.":[62],"This":[63],"gives":[64],"simultaneous":[66],"$(\u03b8,q)$-extension":[67],"Wang--Yang's":[69],"theorems":[70],"for":[71,92],"triangles":[78],"squares.":[80],"further":[82],"establish":[83],"coefficientwise":[84],"nonnegativity":[86],"in":[87],"$q$":[88],"through":[89],"order":[90],"endpoint":[94],"triangles.":[95],"An":[96],"exact":[97],"triangular":[98],"change":[99],"basis":[101],"links":[102],"deformations":[105],"explains":[107],"their":[108],"common":[109],"classical":[110],"limit.":[111]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-23T00:00:00"}