{"id":"https://openalex.org/W2128845692","doi":"https://doi.org/10.37236/1547","title":"A Unified View of Determinantal Expansions for Jack Polynomials","display_name":"A Unified View of Determinantal Expansions for Jack Polynomials","publication_year":2000,"publication_date":"2000-12-29","ids":{"openalex":"https://openalex.org/W2128845692","doi":"https://doi.org/10.37236/1547","mag":"2128845692"},"language":"en","primary_location":{"id":"doi:10.37236/1547","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1547","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r3/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r3/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031859167","display_name":"Leigh Roberts","orcid":null},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Leigh Roberts","raw_affiliation_strings":["School of Economics and Finance Victoria University, P. O. Box 600 Wellington, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Economics and Finance Victoria University, P. O. Box 600 Wellington, New Zealand","institution_ids":["https://openalex.org/I41156924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031859167"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":null,"apc_paid":null,"fwci":1.1683,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.78423773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8136543035507202},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.7530001401901245},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6928569078445435},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.6795623898506165},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.5556448101997375},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5324303507804871},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5155229568481445},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.49549686908721924},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4353753924369812},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.42918989062309265},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42876285314559937},{"id":"https://openalex.org/keywords/elementary-symmetric-polynomial","display_name":"Elementary symmetric polynomial","score":0.4100729823112488},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40642523765563965},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.37315458059310913},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2638707160949707},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12846475839614868},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08726111054420471},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07998448610305786}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8136543035507202},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7530001401901245},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6928569078445435},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.6795623898506165},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.5556448101997375},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5324303507804871},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5155229568481445},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.49549686908721924},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4353753924369812},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.42918989062309265},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42876285314559937},{"id":"https://openalex.org/C64338288","wikidata":"https://www.wikidata.org/wiki/Q2235316","display_name":"Elementary symmetric polynomial","level":4,"score":0.4100729823112488},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40642523765563965},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.37315458059310913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2638707160949707},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12846475839614868},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08726111054420471},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07998448610305786},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1547","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1547","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r3/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":false,"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:10.1.1.22.9573","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.9573","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PDF/v8i1r3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.4399","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.4399","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PostScriptfiles/v8i1r3.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1547","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1547","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r3/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":false,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2128845692.pdf","grobid_xml":"https://content.openalex.org/works/W2128845692.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W655161938","https://openalex.org/W1593259999","https://openalex.org/W2031048748","https://openalex.org/W2087640086","https://openalex.org/W2124818311","https://openalex.org/W2134984950","https://openalex.org/W2156854932"],"related_works":["https://openalex.org/W3161355837","https://openalex.org/W4282813460","https://openalex.org/W4242560508","https://openalex.org/W3060999092","https://openalex.org/W3013709019","https://openalex.org/W185699555","https://openalex.org/W2969359323","https://openalex.org/W4226366657","https://openalex.org/W2901510162","https://openalex.org/W2010067893"],"abstract_inverted_index":{"Recently":[0],"Lapointe":[1],"et.":[2],"al.":[3],"[3]":[4],"have":[5],"expressed":[6],"Jack":[7],"Polynomials":[8],"as":[9,20],"determinants":[10,21,69],"in":[11,22,46],"monomial":[12],"symmetric":[13,24],"functions":[14,25],"$m_\\lambda$.":[15],"We":[16],"express":[17],"these":[18,32],"polynomials":[19],"elementary":[23],"$e_\\lambda$,":[26],"showing":[27],"a":[28],"fundamental":[29],"symmetry":[30],"between":[31],"two":[33],"expansions.":[34],"Moreover,":[35],"both":[36],"expansions":[37],"are":[38,60],"obtained":[39,71],"indifferently":[40],"by":[41],"applying":[42],"the":[43,65,68,73],"Calogero-Sutherland":[44],"operator":[45],"physics":[47],"or":[48],"quasi":[49],"Laplace":[50],"Beltrami":[51],"operators":[52],"arising":[53],"from":[54],"differential":[55],"geometry":[56],"and":[57,62],"statistics.":[58],"Examples":[59],"given,":[61],"comments":[63],"on":[64],"sparseness":[66],"of":[67],"so":[70],"conclude":[72],"paper.":[74]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
