{"id":"https://openalex.org/W1596698480","doi":"https://doi.org/10.37236/528","title":"Counting $k$-Marked Durfee Symbols","display_name":"Counting $k$-Marked Durfee Symbols","publication_year":2010,"publication_date":"2010-02-14","ids":{"openalex":"https://openalex.org/W1596698480","doi":"https://doi.org/10.37236/528","mag":"1596698480"},"language":"en","primary_location":{"id":"doi:10.37236/528","is_oa":true,"landing_page_url":"https://doi.org/10.37236/528","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p41/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/v18i1p41/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043540696","display_name":"Ka\u011fan Kur\u015fung\u00f6z","orcid":"https://orcid.org/0000-0002-4678-5240"},"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":"Ka\u011fan Kur\u015fung\u00f6z","raw_affiliation_strings":["Pennsylvania State Univ#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State Univ#TAB#","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043540696"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.5291,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57164366,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.8954733610153198},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.6564074754714966},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48684948682785034},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.47414180636405945},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4470314383506775},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32900887727737427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30016833543777466},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2948131859302521}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8954733610153198},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.6564074754714966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48684948682785034},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.47414180636405945},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4470314383506775},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32900887727737427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30016833543777466},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2948131859302521},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/528","is_oa":true,"landing_page_url":"https://doi.org/10.37236/528","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p41/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"}],"best_oa_location":{"id":"doi:10.37236/528","is_oa":true,"landing_page_url":"https://doi.org/10.37236/528","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p41/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":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1596698480.pdf","grobid_xml":"https://content.openalex.org/works/W1596698480.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1980668628","https://openalex.org/W2059459845","https://openalex.org/W2068123800","https://openalex.org/W2084912329","https://openalex.org/W2125838758","https://openalex.org/W2329095262","https://openalex.org/W2575871956","https://openalex.org/W2991037217","https://openalex.org/W4234748143","https://openalex.org/W6600858336","https://openalex.org/W6629251564"],"related_works":["https://openalex.org/W4294130366","https://openalex.org/W2613723338","https://openalex.org/W2073931963","https://openalex.org/W2906195750","https://openalex.org/W2801318289","https://openalex.org/W2527515328","https://openalex.org/W3157978488","https://openalex.org/W3119102943","https://openalex.org/W2510751644","https://openalex.org/W2152282046"],"abstract_inverted_index":{"An":[0],"alternative":[1],"characterization":[2],"of":[3,17],"$k$-marked":[4,18],"Durfee":[5,19],"symbols":[6,20,27],"defined":[7],"by":[8,24],"Andrews":[9],"is":[10,40],"given.":[11],"Some":[12],"identities":[13],"involving":[14],"generating":[15],"functions":[16],"are":[21],"proven":[22],"combinatorially":[23],"considering":[25],"the":[26,43],"not":[28],"individually,":[29],"but":[30],"in":[31,42],"equivalence":[32],"classes.":[33],"Also,":[34],"a":[35],"related":[36],"binomial":[37],"coefficient":[38],"identity":[39],"obtained":[41],"course.":[44]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}