{"id":"https://openalex.org/W1597164615","doi":"https://doi.org/10.37236/545","title":"Ramanujan Type Congruences for a Partition Function","display_name":"Ramanujan Type Congruences for a Partition Function","publication_year":2011,"publication_date":"2011-03-11","ids":{"openalex":"https://openalex.org/W1597164615","doi":"https://doi.org/10.37236/545","mag":"1597164615"},"language":"en","primary_location":{"id":"doi:10.37236/545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/545","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p58/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/v18i1p58/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030527371","display_name":"Haijian Zhao","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":"Haijian Zhao","raw_affiliation_strings":["Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058476389","display_name":"Zheyuan Zhong","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":"Zheyuan Zhong","raw_affiliation_strings":["Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China","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":4.7475,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9489241,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"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/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":0.9998000264167786,"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":0.9944000244140625,"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/congruence-relation","display_name":"Congruence relation","score":0.907666802406311},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8950793743133545},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.8306335210800171},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.758355975151062},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6394342184066772},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5758649706840515},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4998435974121094},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4341876208782196},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.4276464879512787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3332942724227905},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0450800359249115}],"concepts":[{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.907666802406311},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8950793743133545},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.8306335210800171},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.758355975151062},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6394342184066772},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5758649706840515},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4998435974121094},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4341876208782196},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.4276464879512787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3332942724227905},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0450800359249115},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/545","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p58/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:10.1.1.372.6091","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.6091","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/ojs/index.php/eljc/article/viewFile/v18i1p58/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/545","is_oa":true,"landing_page_url":"https://doi.org/10.37236/545","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p58/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/W1597164615.pdf","grobid_xml":"https://content.openalex.org/works/W1597164615.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1601940535","https://openalex.org/W1997768198","https://openalex.org/W2028657516","https://openalex.org/W2040573691","https://openalex.org/W2166762532","https://openalex.org/W4294576164"],"related_works":["https://openalex.org/W1488291224","https://openalex.org/W3215838177","https://openalex.org/W2081852078","https://openalex.org/W2945221657","https://openalex.org/W2917145361","https://openalex.org/W4301228773","https://openalex.org/W2951833366","https://openalex.org/W1990165672","https://openalex.org/W2084001194","https://openalex.org/W2011465559"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2],"arithmetic":[3],"properties":[4],"of":[5,15],"a":[6],"certain":[7],"function":[8],"$b(n)$":[9],"given":[10],"by":[11],"$\\sum\\limits_{n=0}^\\infty":[12],"b(n)q^n=(q;q)_\\infty^{-2}(q^2;q^2)_\\infty^{-2}$.":[13],"One":[14],"our":[16],"main":[17],"results":[18],"is":[19],"$b(9n+7)\\equiv":[20],"0\\":[21],"({\\rm":[22],"mod\\":[23],"}9)$.":[24]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
