{"id":"https://openalex.org/W1939879739","doi":"https://doi.org/10.37236/5473","title":"Simultaneous Core Partitions: Parameterizations and Sums","display_name":"Simultaneous Core Partitions: Parameterizations and Sums","publication_year":2016,"publication_date":"2016-01-11","ids":{"openalex":"https://openalex.org/W1939879739","doi":"https://doi.org/10.37236/5473","mag":"1939879739"},"language":"en","primary_location":{"id":"doi:10.37236/5473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p4/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/v23i1p4/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019197959","display_name":"Victor Y. Wang","orcid":"https://orcid.org/0000-0002-0704-7026"},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Victor Y. Wang","raw_affiliation_strings":["MIT"],"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I4210109586"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019197959"],"corresponding_institution_ids":["https://openalex.org/I4210109586"],"apc_list":null,"apc_paid":null,"fwci":1.3272,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7575188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"1","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/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":0.9986000061035156,"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/conjecture","display_name":"Conjecture","score":0.8850153088569641},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.8725419044494629},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6949154138565063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6482682228088379},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5992870330810547},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.4616836905479431},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.44354793429374695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33802956342697144},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15896978974342346},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10293444991111755}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8850153088569641},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.8725419044494629},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6949154138565063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6482682228088379},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5992870330810547},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4616836905479431},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.44354793429374695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33802956342697144},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15896978974342346},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10293444991111755},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/5473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p4/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:1507.04290","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.04290","pdf_url":"https://arxiv.org/pdf/1507.04290","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":null,"raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/103038","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/103038","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"European Mathematical Information Service (EMIS)","raw_type":"http://purl.org/eprint/type/JournalArticle"},{"id":"doi:10.48550/arxiv.1507.04290","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.04290","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-journal"},{"id":"mag:1939879739","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/5473","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5473","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p4/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/G2185199909","display_name":null,"funder_award_id":"1358695","funder_id":"https://openalex.org/F4320311500","funder_display_name":"University of Minnesota Duluth"},{"id":"https://openalex.org/G3213978052","display_name":null,"funder_award_id":"H98230-13-1-0273","funder_id":"https://openalex.org/F4320311500","funder_display_name":"University of Minnesota Duluth"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G968230921","display_name":null,"funder_award_id":"1358695","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/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311500","display_name":"University of Minnesota Duluth","ror":"https://ror.org/01hy4qx27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1939879739.pdf","grobid_xml":"https://content.openalex.org/works/W1939879739.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1646261715","https://openalex.org/W1666201387","https://openalex.org/W1906094349","https://openalex.org/W1965115466","https://openalex.org/W1990623507","https://openalex.org/W1993440568","https://openalex.org/W1994230987","https://openalex.org/W2023592012","https://openalex.org/W2029909197","https://openalex.org/W2075325208","https://openalex.org/W2078766864","https://openalex.org/W2079602836","https://openalex.org/W2091292741","https://openalex.org/W2108971346","https://openalex.org/W2122432245","https://openalex.org/W2156669497","https://openalex.org/W2184542655","https://openalex.org/W2514823897","https://openalex.org/W2949868547","https://openalex.org/W2962805952","https://openalex.org/W2962895140","https://openalex.org/W2962926841","https://openalex.org/W2963954687","https://openalex.org/W6601356614","https://openalex.org/W6602536545","https://openalex.org/W6607578273","https://openalex.org/W6699982930"],"related_works":["https://openalex.org/W3097848819","https://openalex.org/W1826866960","https://openalex.org/W3213614370","https://openalex.org/W3010990195","https://openalex.org/W3083543409","https://openalex.org/W3092806484","https://openalex.org/W3093881334","https://openalex.org/W3102618960","https://openalex.org/W2322437738","https://openalex.org/W2951261247","https://openalex.org/W2953506835","https://openalex.org/W2032359312","https://openalex.org/W2951278237","https://openalex.org/W2031774185","https://openalex.org/W3103870832","https://openalex.org/W2949180070","https://openalex.org/W2804505440","https://openalex.org/W2591592591","https://openalex.org/W1941200707","https://openalex.org/W2953268926"],"abstract_inverted_index":{"Fix":[0],"coprime":[1,158],"$s,t\\ge1$.":[2],"We":[3,41,72],"re-prove,":[4],"without":[5],"Ehrhart":[6],"reciprocity,":[7],"a":[8,44,66,161],"conjecture":[9,46,76,163],"of":[10,30,47,62,65,110,131,155,164],"Armstrong":[11],"(recently":[12],"verified":[13],"by":[14,39,53],"Johnson)":[15],"that":[16,27,49,77,117,135],"the":[17,28,34,50,59,63,78,83,118,136,153],"finitely":[18],"many":[19],"simultaneous":[20],"$(s,t)$-cores":[21],"have":[22,124],"average":[23,36,51,81],"size":[24,61],"$\\frac{1}{24}(s-1)(t-1)(s+t+1)$,":[25],"and":[26,166],"subset":[29],"self-conjugate":[31,80],"cores":[32],"has":[33],"same":[35,84],"(first":[37],"shown":[38],"Chen-Huang-Wang).":[40],"similarly":[42],"prove":[43,74],"recent":[45,162],"Fayers":[48],"weighted":[52],"an":[54,144],"inverse":[55],"stabilizer":[56],"-":[57,69,101,106],"giving":[58],"\"expected":[60],"$t$-core":[64],"random":[67],"$s$-core\"":[68],"is":[70,82,87,94,116],"$\\frac{1}{24}(s-1)(t^2-1)$.":[71],"also":[73,133],"Fayers'":[75,122],"analogous":[79],"if":[85,92],"$t$":[86,93],"odd,":[88],"but":[89],"instead":[90],"$\\frac{1}{24}(s-1)(t^2+2)$":[91],"even.":[95],"In":[96],"principle,":[97],"our":[98],"explicit":[99],"methods":[100],"or":[102],"implicit":[103],"variants":[104],"thereof":[105],"extend":[107,138],"to":[108,139],"averages":[109],"arbitrary":[111],"powers.The":[112],"main":[113],"new":[114],"observation":[115],"stabilizers":[119],"appearing":[120],"in":[121,127],"conjectures":[123],"simple":[125],"formulas":[126],"Johnson's":[128],"$z$-coordinates":[129,137],"parameterization":[130],"$(s,t)$-cores.We":[132],"observe":[134],"parameterize":[140],"general":[141],"$t$-cores.":[142],"As":[143],"example":[145],"application":[146],"with":[147],"$t":[148],":=":[149],"s+d$,":[150],"we":[151],"count":[152],"number":[154],"$(s,s+d,s+2d)$-cores":[156],"for":[157],"$s,d\\ge1$,":[159],"verifying":[160],"Amdeberhan":[165],"Leven.":[167]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}