{"id":"https://openalex.org/W1836054608","doi":"https://doi.org/10.37236/1858","title":"On a Partition Function of Richard Stanley","display_name":"On a Partition Function of Richard Stanley","publication_year":2004,"publication_date":"2004-06-03","ids":{"openalex":"https://openalex.org/W1836054608","doi":"https://doi.org/10.37236/1858","mag":"1836054608"},"language":"en","primary_location":{"id":"doi:10.37236/1858","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1858","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r1/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/v11i2r1/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055200378","display_name":"George E. Andrews","orcid":"https://orcid.org/0000-0002-8909-823X"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George E. Andrews","raw_affiliation_strings":["Department of Mathematics The Pennsylvania State University University Park, PA 16802"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics The Pennsylvania State University University Park, PA 16802","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055200378"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":6.5414,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.97046263,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9973000288009644,"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":0.9902999997138977,"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/ramanujans-sum","display_name":"Ramanujan's sum","score":0.8565689325332642},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8008456230163574},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7826417088508606},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7094753980636597},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.6991465091705322},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5259022116661072},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.5229347944259644},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.5040382742881775},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.4539889097213745},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.4242822229862213},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42225730419158936},{"id":"https://openalex.org/keywords/theta-function","display_name":"Theta function","score":0.4222356677055359},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.42201468348503113},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1586913764476776},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06288376450538635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05692240595817566},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.056307703256607056}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.8565689325332642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8008456230163574},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7826417088508606},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7094753980636597},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.6991465091705322},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5259022116661072},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.5229347944259644},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.5040382742881775},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.4539889097213745},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.4242822229862213},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42225730419158936},{"id":"https://openalex.org/C105546189","wikidata":"https://www.wikidata.org/wiki/Q1154787","display_name":"Theta function","level":2,"score":0.4222356677055359},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.42201468348503113},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1586913764476776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06288376450538635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05692240595817566},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.056307703256607056},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1858","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1858","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r1/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:10.1.1.159.7016","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.7016","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_11/PDF/v11i2r1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.87.1137","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.1137","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/stanley.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1858","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1858","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i2r1/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":[{"id":"https://openalex.org/G7183835584","display_name":"Number Theory and Combinatorics","funder_award_id":"0200047","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1836054608.pdf","grobid_xml":"https://content.openalex.org/works/W1836054608.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1489188437","https://openalex.org/W1977434798","https://openalex.org/W1995036763","https://openalex.org/W1995945562","https://openalex.org/W2008052995","https://openalex.org/W2024366676","https://openalex.org/W2038537842","https://openalex.org/W2050976572","https://openalex.org/W2054811772","https://openalex.org/W2070308814","https://openalex.org/W2076597612","https://openalex.org/W2105863811","https://openalex.org/W2125838758","https://openalex.org/W2152754892","https://openalex.org/W2162955405","https://openalex.org/W2914782162","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W3215838177","https://openalex.org/W1488291224","https://openalex.org/W2081852078","https://openalex.org/W2945221657","https://openalex.org/W4301228773","https://openalex.org/W2951833366","https://openalex.org/W2917145361","https://openalex.org/W2084001194","https://openalex.org/W2952551384","https://openalex.org/W2999033040"],"abstract_inverted_index":{"In":[0],"this":[1,49],"paper,":[2],"we":[3],"examine":[4],"partitions":[5,36],"$\\pi$":[6,17,43],"classified":[7],"according":[8],"to":[9],"the":[10,20,27,40],"number":[11,21],"$r(\\pi)$":[12],"of":[13,22,29,42,52],"odd":[14,23],"parts":[15,24,41],"in":[16,25],"and":[18],"$s(\\pi)$":[19],"$\\pi\\prime$,":[26],"conjugate":[28],"$\\pi$.":[30],"The":[31],"generating":[32],"function":[33,63],"for":[34,60],"such":[35],"is":[37],"obtained":[38],"when":[39],"are":[44],"all":[45],"$\\leq":[46],"N$.":[47],"From":[48],"a":[50,56],"variety":[51],"corollaries":[53],"follow":[54],"including":[55],"Ramanujan":[57],"type":[58],"congruence":[59],"Stanley's":[61],"partition":[62],"$t(n)$.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
