{"id":"https://openalex.org/W2991886201","doi":"https://doi.org/10.37236/2026","title":"On the Zeros of Plane Partition Polynomials","display_name":"On the Zeros of Plane Partition Polynomials","publication_year":2012,"publication_date":"2012-01-02","ids":{"openalex":"https://openalex.org/W2991886201","doi":"https://doi.org/10.37236/2026","mag":"2991886201"},"language":"en","primary_location":{"id":"doi:10.37236/2026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i2p30/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/v18i2p30/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021269361","display_name":"Robert P. Boyer","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert P. Boyer","raw_affiliation_strings":["Department of Mathematics Drexel University Philadelphia, PA 19104"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Drexel University Philadelphia, PA 19104","institution_ids":["https://openalex.org/I72816309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042264762","display_name":"Daniel Parry","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel T. Parry","raw_affiliation_strings":["Department of Mathematics Drexel University Philadelphia, PA 19104"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Drexel University Philadelphia, PA 19104","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021269361"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":2.9146,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9134637,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9991000294685364,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9988999962806702,"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":0.8733993768692017},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8153799772262573},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7174592614173889},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.6904952526092529},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6327494382858276},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6050064563751221},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5632925629615784},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5615489482879639},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.49139299988746643},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.4775339365005493},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4703773856163025},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.4153348505496979},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4109746813774109},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3645106852054596},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.232184499502182},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20705071091651917}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8733993768692017},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8153799772262573},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7174592614173889},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.6904952526092529},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6327494382858276},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6050064563751221},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5632925629615784},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5615489482879639},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.49139299988746643},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.4775339365005493},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4703773856163025},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.4153348505496979},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4109746813774109},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3645106852054596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.232184499502182},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20705071091651917},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i2p30/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:10.37236/2026","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2026","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i2p30/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2991886201.pdf","grobid_xml":"https://content.openalex.org/works/W2991886201.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1513070183","https://openalex.org/W1832583097","https://openalex.org/W1972890801","https://openalex.org/W2000101905","https://openalex.org/W2006496110","https://openalex.org/W2019698057","https://openalex.org/W2051444432","https://openalex.org/W2124870776","https://openalex.org/W2130504407","https://openalex.org/W2132942077","https://openalex.org/W2171498853","https://openalex.org/W2331275820","https://openalex.org/W2802739963","https://openalex.org/W3043060850","https://openalex.org/W3144829920","https://openalex.org/W4299533062","https://openalex.org/W4301171592"],"related_works":["https://openalex.org/W4235718433","https://openalex.org/W2056801132","https://openalex.org/W1982796873","https://openalex.org/W1971346124","https://openalex.org/W2329676358","https://openalex.org/W4200559628","https://openalex.org/W4287124158","https://openalex.org/W1602558449","https://openalex.org/W1985478951","https://openalex.org/W2075590417"],"abstract_inverted_index":{"Let":[0],"$PL(n)$":[1],"be":[2,13],"the":[3,14,28,45,57,61,70,81,89],"number":[4,15],"of":[5,9,16,19,30,34,60,63,69],"all":[6],"plane":[7,17,35],"partitions":[8,18,36],"$n$":[10,20,87],"while":[11,84],"$pp_k(n)$":[12],"whose":[21],"trace":[22],"is":[23],"exactly":[24],"$k$.":[25],"We":[26],"study":[27],"zeros":[29,62,71],"polynomial":[31],"versions":[32],"$Q_n(x)$":[33,51,64],"where":[37],"$Q_n(x)":[38],"=":[39],"\\sum":[40],"pp_k(n)":[41],"x^k$.":[42],"Based":[43],"on":[44,88],"asymptotics":[46],"we":[47,55],"have":[48],"developed":[49],"for":[50],"and":[52],"computational":[53],"evidence,":[54],"determine":[56],"limiting":[58],"behavior":[59,75],"as":[65],"$n\\to\\infty$.":[66],"The":[67],"distribution":[68],"has":[72,77,85],"a":[73],"two-scale":[74],"which":[76],"order":[78,86],"$n^{2/3}$":[79],"inside":[80],"unit":[82,90],"disk":[83],"circle.":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
