{"id":"https://openalex.org/W1890354621","doi":"https://doi.org/10.37236/1861","title":"Orthogonal Polynomials Represented by $CW$-Spheres","display_name":"Orthogonal Polynomials Represented by $CW$-Spheres","publication_year":2004,"publication_date":"2004-08-16","ids":{"openalex":"https://openalex.org/W1890354621","doi":"https://doi.org/10.37236/1861","mag":"1890354621"},"language":"en","primary_location":{"id":"doi:10.37236/1861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r4/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/v11i2r4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089863827","display_name":"G\u00e1bor Hetyei","orcid":"https://orcid.org/0000-0003-3596-6289"},"institutions":[{"id":"https://openalex.org/I102149020","display_name":"University of North Carolina at Charlotte","ror":"https://ror.org/04dawnj30","country_code":"US","type":"education","lineage":["https://openalex.org/I102149020"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["HU","SK","US"],"is_corresponding":true,"raw_author_name":"G\u00e1bor Hetyei","raw_affiliation_strings":["Mathematics Department UNC Charlotte Charlotte, NC 28223","Rnyi Mathematical Institute of the Hungarian Academy of Sciences","R\u00e9nyi Mathematical Institute of the Hungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Mathematics Department UNC Charlotte Charlotte, NC 28223","institution_ids":["https://openalex.org/I102149020"]},{"raw_affiliation_string":"Rnyi Mathematical Institute of the Hungarian Academy of Sciences","institution_ids":[]},{"raw_affiliation_string":"R\u00e9nyi Mathematical Institute of the Hungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260","https://openalex.org/I4210120676"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089863827"],"corresponding_institution_ids":["https://openalex.org/I102149020","https://openalex.org/I127817813","https://openalex.org/I4210120676","https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":2.0681,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82840524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"2","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":0.9998999834060669,"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":0.9998000264167786,"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":0.9994000196456909,"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":0.8192251920700073},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7209609150886536},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.5618703961372375},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5436716079711914},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.516758382320404},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4761921465396881},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.45682504773139954},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4545343518257141},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4260771870613098},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38522130250930786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1465267837047577},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09652242064476013},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09337413311004639}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8192251920700073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7209609150886536},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.5618703961372375},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5436716079711914},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.516758382320404},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4761921465396881},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.45682504773139954},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4545343518257141},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4260771870613098},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38522130250930786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1465267837047577},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09652242064476013},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09337413311004639},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r4/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.6358","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.6358","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_11/PDF/v11i2r4.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1861","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1861","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r4/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1890354621.pdf","grobid_xml":"https://content.openalex.org/works/W1890354621.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W608832534","https://openalex.org/W1546959834","https://openalex.org/W1565240535","https://openalex.org/W1966268321","https://openalex.org/W1981389494","https://openalex.org/W1990911204","https://openalex.org/W1994713714","https://openalex.org/W2001367217","https://openalex.org/W2008933953","https://openalex.org/W2054009182","https://openalex.org/W2063998480","https://openalex.org/W2128633210","https://openalex.org/W2134937349","https://openalex.org/W2144713557","https://openalex.org/W2334336952","https://openalex.org/W4205498891","https://openalex.org/W4384817650","https://openalex.org/W7029223938"],"related_works":["https://openalex.org/W2115188219","https://openalex.org/W4280542807","https://openalex.org/W3130526622","https://openalex.org/W4256532491","https://openalex.org/W75320130","https://openalex.org/W4287754054","https://openalex.org/W4288725121","https://openalex.org/W3034218783","https://openalex.org/W2885676679","https://openalex.org/W2150914572"],"abstract_inverted_index":{"Given":[0],"a":[1,10,25,34,60,132],"sequence":[2,26],"$\\{Q_n(x)\\}_{n=0}^{\\infty}$":[3],"of":[4,27,37,46,49,66,68,76,79,97,99,148,154],"symmetric":[5],"orthogonal":[6,90,155],"polynomials,":[7],"defined":[8],"by":[9],"recurrence":[11],"formula":[12],"$Q_n(x)=\\nu_n\\cdot":[13],"x\\cdot":[14],"Q_{n-1}(x)-(\\nu_n-1)\\cdot":[15],"Q_{n-2}(x)$":[16],"with":[17],"integer":[18],"$\\nu_i$'s":[19,113],"satisfying":[20],"$\\nu_i\\geq":[21],"2$,":[22],"we":[23,54],"construct":[24],"nested":[28],"Eulerian":[29,52,160],"posets":[30,53],"whose":[31],"$ce$-index":[32],"is":[33,121,127],"non-commutative":[35],"generalization":[36],"these":[38],"polynomials.":[39],"Using":[40],"spherical":[41],"shellings":[42],"and":[43,117,144,157],"direct":[44],"calculations":[45,84],"the":[47,50,63,74,77,89,100,109,112,118,146,152],"$cd$-coefficients":[48],"associated":[51],"obtain":[55],"two":[56],"new":[57,133],"proofs":[58,104],"for":[59,137,141],"bound":[61],"on":[62],"true":[64],"interval":[65],"orthogonality":[67],"$\\{Q_n(x)\\}_{n=0}^{\\infty}$.":[69],"Either":[70],"argument":[71],"can":[72],"replace":[73],"use":[75],"theory":[78,153],"chain":[80],"sequences.":[81],"Our":[82],"$cd$-index":[83],"allow":[85],"us":[86],"to":[87,108],"represent":[88],"polynomials":[91,156],"as":[92],"an":[93],"explicit":[94],"positive":[95],"combination":[96],"terms":[98],"form":[101],"$x^{n-2r}(x^2-1)^r$.":[102],"Both":[103],"may":[105],"be":[106],"extended":[107],"case":[110],"when":[111,124],"are":[114],"not":[115],"integers":[116],"second":[119],"proof":[120],"still":[122],"valid":[123],"only":[125],"$\\nu_i>1$":[126],"required.":[128],"The":[129],"construction":[130],"provides":[131],"\"limited":[134],"testing":[135],"ground\"":[136],"Stanley's":[138],"non-negativity":[139],"conjecture":[140],"Gorenstein$^*$":[142],"posets,":[143],"suggests":[145],"existence":[147],"strong":[149],"links":[150],"between":[151],"flag-enumeration":[158],"in":[159],"posets.":[161]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}