{"id":"https://openalex.org/W2581366231","doi":"https://doi.org/10.37236/9011","title":"Macdonald Polynomials and Chromatic Quasisymmetric Functions","display_name":"Macdonald Polynomials and Chromatic Quasisymmetric Functions","publication_year":2020,"publication_date":"2020-08-21","ids":{"openalex":"https://openalex.org/W2581366231","doi":"https://doi.org/10.37236/9011","mag":"2581366231"},"language":"en","primary_location":{"id":"doi:10.37236/9011","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9011","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p37/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p37/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111371005","display_name":"James Haglund","orcid":null},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Haglund","raw_affiliation_strings":["University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014375002","display_name":"Andrew Timothy Wilson","orcid":"https://orcid.org/0000-0003-1325-2867"},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Timothy Wilson","raw_affiliation_strings":["University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6427,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7763765,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"3","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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9983999729156494,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9891999959945679,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.7850950956344604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7763612866401672},{"id":"https://openalex.org/keywords/schur-polynomial","display_name":"Schur polynomial","score":0.7125495076179504},{"id":"https://openalex.org/keywords/koornwinder-polynomials","display_name":"Koornwinder polynomials","score":0.630150318145752},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.5843756198883057},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.5404596328735352},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5313423871994019},{"id":"https://openalex.org/keywords/power-sum-symmetric-polynomial","display_name":"Power sum symmetric polynomial","score":0.5114413499832153},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5032386183738708},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.4770573675632477},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.448917418718338},{"id":"https://openalex.org/keywords/wilson-polynomials","display_name":"Wilson polynomials","score":0.44743624329566956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43097203969955444},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.429246187210083}],"concepts":[{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.7850950956344604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7763612866401672},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.7125495076179504},{"id":"https://openalex.org/C5056958","wikidata":"https://www.wikidata.org/wiki/Q6430769","display_name":"Koornwinder polynomials","level":5,"score":0.630150318145752},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.5843756198883057},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.5404596328735352},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5313423871994019},{"id":"https://openalex.org/C129010115","wikidata":"https://www.wikidata.org/wiki/Q1298683","display_name":"Power sum symmetric polynomial","level":5,"score":0.5114413499832153},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5032386183738708},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.4770573675632477},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.448917418718338},{"id":"https://openalex.org/C43176163","wikidata":"https://www.wikidata.org/wiki/Q8023263","display_name":"Wilson polynomials","level":4,"score":0.44743624329566956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43097203969955444},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.429246187210083}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9011","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9011","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p37/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1701.05622","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.05622","pdf_url":"https://arxiv.org/pdf/1701.05622","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":null},{"id":"mag:2581366231","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1701.05622.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1701.05622","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1701.05622","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/9011","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9011","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p37/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5740760286","display_name":"Combinatorics of Symmetric Functions","funder_award_id":"1200296","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7202345784","display_name":null,"funder_award_id":"DMS-1200296","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2581366231.pdf","grobid_xml":"https://content.openalex.org/works/W2581366231.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W594004768","https://openalex.org/W1648811467","https://openalex.org/W1671066123","https://openalex.org/W1853497194","https://openalex.org/W1986584245","https://openalex.org/W1994361587","https://openalex.org/W2001124661","https://openalex.org/W2006224450","https://openalex.org/W2021646443","https://openalex.org/W2040741400","https://openalex.org/W2064406668","https://openalex.org/W2134984950","https://openalex.org/W2143512497","https://openalex.org/W2331950050","https://openalex.org/W2573960099","https://openalex.org/W2963339095","https://openalex.org/W2963579220","https://openalex.org/W6765538143"],"related_works":["https://openalex.org/W3083496953","https://openalex.org/W2992045920","https://openalex.org/W2952592793","https://openalex.org/W2952560466","https://openalex.org/W3197350509","https://openalex.org/W2735654422","https://openalex.org/W815153619","https://openalex.org/W2949274139","https://openalex.org/W1888546338","https://openalex.org/W2952634831","https://openalex.org/W1614187983","https://openalex.org/W2962912149","https://openalex.org/W2990859661","https://openalex.org/W2129979922","https://openalex.org/W3106280648","https://openalex.org/W2021646443","https://openalex.org/W3101714663","https://openalex.org/W3049904845","https://openalex.org/W2331950050","https://openalex.org/W2975633790"],"abstract_inverted_index":{"We":[0],"express":[1],"the":[2,46,52],"integral":[3,47,61],"form":[4,48,62],"Macdonald":[5,49,63],"polynomials":[6,56,71],"as":[7,72],"a":[8,58],"weighted":[9],"sum":[10,35,43],"of":[11,18,26,60],"Shareshian":[12],"and":[13,33,41],"Wachs'":[14],"chromatic":[15,28],"quasisymmetric":[16,29],"functions":[17,30,37],"certain":[19],"graphs.":[20],"Then":[21],"we":[22,65],"use":[23],"known":[24],"expansions":[25],"these":[27],"into":[31],"Schur":[32,40],"power":[34,42],"symmetric":[36],"to":[38],"provide":[39],"formulas":[44,68],"for":[45,69],"polynomials.":[50],"Since":[51],"(integral":[53],"form)":[54],"Jack":[55,70],"are":[57],"specialization":[59],"polynomials,":[64],"obtain":[66],"analogous":[67],"corollaries.":[73]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}