{"id":"https://openalex.org/W2106900447","doi":"https://doi.org/10.37236/488","title":"On the Modes of Polynomials Derived from Nondecreasing Sequences","display_name":"On the Modes of Polynomials Derived from Nondecreasing Sequences","publication_year":2011,"publication_date":"2011-01-05","ids":{"openalex":"https://openalex.org/W2106900447","doi":"https://doi.org/10.37236/488","mag":"2106900447"},"language":"en","primary_location":{"id":"doi:10.37236/488","is_oa":true,"landing_page_url":"https://doi.org/10.37236/488","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p1/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035094982","display_name":"Donna Q. J. Dou","orcid":"https://orcid.org/0000-0002-8894-2443"},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]},{"id":"https://openalex.org/I4210136497","display_name":"Jilin Medical University","ror":"https://ror.org/03mzw7781","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210136497"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Donna Q. J. Dou","raw_affiliation_strings":["School of Mathematics Jilin University, Changchun 130012, P. R. China","jilin University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics Jilin University, Changchun 130012, P. R. China","institution_ids":["https://openalex.org/I194450716"]},{"raw_affiliation_string":"jilin University","institution_ids":["https://openalex.org/I4210136497"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113340209","display_name":"Arthur L. B. Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Arthur L. B. Yang","raw_affiliation_strings":["Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin 300071, P. R. China","Nankai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin 300071, P. R. China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Nankai University","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2397,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86564838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"1","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":0.9988999962806702,"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":0.9988999962806702,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8862550258636475},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8394302129745483},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8210567235946655},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6121575236320496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3782269358634949},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12466362118721008}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8862550258636475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8394302129745483},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8210567235946655},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6121575236320496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3782269358634949},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12466362118721008}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/488","is_oa":true,"landing_page_url":"https://doi.org/10.37236/488","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/488","is_oa":true,"landing_page_url":"https://doi.org/10.37236/488","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p1/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2106900447.pdf","grobid_xml":"https://content.openalex.org/works/W2106900447.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1521247755","https://openalex.org/W1592542709","https://openalex.org/W2022865944","https://openalex.org/W2111812366","https://openalex.org/W2112054149","https://openalex.org/W3104983062"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Wang":[0,56],"and":[1,12,51,57,66],"Yeh":[2,58],"proved":[3],"that":[4,36,43,60],"if":[5,61],"$P(x)$":[6],"is":[7,17,31,38,45],"a":[8,25,71],"polynomial":[9,27],"with":[10],"nonnegative":[11],"nondecreasing":[13],"coefficients,":[14],"then":[15,63],"$P(x+d)$":[16],"unimodal":[18,26],"for":[19],"any":[20],"$d>0$.":[21],"A":[22],"mode":[23,48],"of":[24,49,73],"$f(x)=a_0+a_1x+\\cdots":[28],"+":[29],"a_mx^m$":[30],"an":[32],"index":[33],"$k$":[34],"such":[35],"$a_k$":[37],"the":[39,46,53],"maximum":[40],"coefficient.":[41],"Suppose":[42],"$M_*(P,d)$":[44],"smallest":[47],"$P(x+d)$,":[50],"$M^*(P,d)$":[52],"greatest":[54],"mode.":[55],"conjectured":[59],"$d_2>d_1>0$,":[62],"$M_*(P,d_1)\\geq":[64],"M_*(P,d_2)$":[65],"$M^*(P,d_1)\\geq":[67],"M^*(P,d_2)$.":[68],"We":[69],"give":[70],"proof":[72],"this":[74],"conjecture.":[75]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}