{"id":"https://openalex.org/W2963657376","doi":"https://doi.org/10.1137/16m1101866","title":"Positivity of Iterated Sequences of Polynomials","display_name":"Positivity of Iterated Sequences of Polynomials","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2963657376","doi":"https://doi.org/10.1137/16m1101866","mag":"2963657376"},"language":"en","primary_location":{"id":"doi:10.1137/16m1101866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1101866","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete 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/A5091531217","display_name":"Bao-Xuan Zhu","orcid":"https://orcid.org/0000-0002-3682-6184"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bao-Xuan Zhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5091531217"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.1096,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.99279869,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"3","first_page":"1993","last_page":"2010"},"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":0.9990000128746033,"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":0.9908000230789185,"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/convexity","display_name":"Convexity","score":0.8450957536697388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8253697752952576},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7880739569664001},{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.6674627065658569},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6417909860610962},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.5201221704483032},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5179752111434937},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.4850415587425232},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43174445629119873},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4207311272621155},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16156265139579773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.102763831615448}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8450957536697388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8253697752952576},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7880739569664001},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.6674627065658569},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6417909860610962},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.5201221704483032},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5179752111434937},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.4850415587425232},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43174445629119873},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4207311272621155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16156265139579773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.102763831615448},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1101866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1101866","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2380745065","display_name":"\u7ec4\u5408\u5e8f\u5217\u7684\u6b63\u6027\u7814\u7a76","funder_award_id":"11571150","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1754892739","https://openalex.org/W1967472879","https://openalex.org/W1972006298","https://openalex.org/W1980944648","https://openalex.org/W1994416105","https://openalex.org/W2014724230","https://openalex.org/W2017381362","https://openalex.org/W2021347618","https://openalex.org/W2033428949","https://openalex.org/W2035133303","https://openalex.org/W2046479912","https://openalex.org/W2050274205","https://openalex.org/W2051330046","https://openalex.org/W2054833597","https://openalex.org/W2055840522","https://openalex.org/W2068045918","https://openalex.org/W2072729208","https://openalex.org/W2072875206","https://openalex.org/W2076071550","https://openalex.org/W2076114419","https://openalex.org/W2084587471","https://openalex.org/W2090824304","https://openalex.org/W2091216084","https://openalex.org/W2105521920","https://openalex.org/W2107406456","https://openalex.org/W2149977129","https://openalex.org/W2151257138","https://openalex.org/W2154951927","https://openalex.org/W2461823106","https://openalex.org/W2748602324","https://openalex.org/W2953301595","https://openalex.org/W2963236270","https://openalex.org/W2963369124","https://openalex.org/W3101140896","https://openalex.org/W4207036379","https://openalex.org/W4250083519"],"related_works":["https://openalex.org/W2551082991","https://openalex.org/W3102813141","https://openalex.org/W2083685161","https://openalex.org/W1557127993","https://openalex.org/W2418411990","https://openalex.org/W2387850874","https://openalex.org/W2165966680","https://openalex.org/W2896175204","https://openalex.org/W2810013662","https://openalex.org/W2963657376"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"some":[5],"criteria":[6,43],"for":[7,133],"the":[8,20,38,60,77,80,88,94,102,108,115,121],"2-$q$-log-convexity":[9,61],"and":[10,51,70,86,100,113,125],"3-$q$-log-convexity":[11,71],"of":[12,23,30,59,62,67,72,83,97,105,111,118],"combinatorial":[13],"sequences,":[14],"which":[15,128],"can":[16,44],"be":[17,46],"regarded":[18],"as":[19],"first":[21],"column":[22],"a":[24,56],"certain":[25],"infinite":[26],"triangular":[27],"array":[28],"$[A_{n,k}(q)]_{n,k\\geq0}$":[29],"polynomials":[31,82,96],"in":[32,107,120],"$q$":[33],"with":[34],"nonnegative":[35],"coefficients":[36],"satisfying":[37],"recurrence":[39],"relation":[40],"$A_{n,k}(q)=A_{n-1,k-1}(q)+g_k(q)A_{n-1,k}(q)+h_{k+1}(q)A_{n-1,k+1}(q).$":[41],"Those":[42],"also":[45],"presented":[47],"by":[48],"continued":[49],"fractions":[50],"generating":[52,103,116],"functions.":[53],"These":[54],"allow":[55],"unified":[57],"treatment":[58],"alternating":[63],"Eulerian":[64,81],"polynomials,":[65,75,79],"2-log-convexity":[66],"Euler":[68],"numbers,":[69,90,93],"many":[73,130],"classical":[74],"including":[76],"Bell":[78],"types":[84,98],"$A$":[85,99],"$B$,":[87,101],"$q$-Schr\u00f6der":[89],"$q$-central":[91],"Delannoy":[92],"Narayana":[95],"functions":[104,117],"rows":[106,119],"Catalan":[109],"triangles":[110],"Aigner":[112],"Shapiro,":[114],"large":[122],"Schr\u00f6der":[123],"triangle,":[124],"so":[126],"on,":[127],"extend":[129],"known":[131],"results":[132],"$q$-log-convexity.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
