{"id":"https://openalex.org/W1582170611","doi":"https://doi.org/10.37236/1484","title":"A Note on the Symmetric Powers of the Standard Representation of $S_n$","display_name":"A Note on the Symmetric Powers of the Standard Representation of $S_n$","publication_year":2000,"publication_date":"2000-02-12","ids":{"openalex":"https://openalex.org/W1582170611","doi":"https://doi.org/10.37236/1484","mag":"1582170611"},"language":"en","primary_location":{"id":"doi:10.37236/1484","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1484","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r6/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r6/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006934714","display_name":"David Savitt","orcid":"https://orcid.org/0000-0001-5761-1177"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Savitt","raw_affiliation_strings":["Department of Mathematics, Harvard University Cambridge, MA 02138, USA","Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvard University Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110170055","display_name":"R. P. Stanley","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. P. Stanley","raw_affiliation_strings":["Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006934714"],"corresponding_institution_ids":["https://openalex.org/I136199984","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.08317699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","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":1.0,"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":1.0,"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":0.9980999827384949,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8990775942802429},{"id":"https://openalex.org/keywords/span","display_name":"Span (engineering)","score":0.7795878648757935},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.771222710609436},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6819807887077332},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.613868772983551},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5953177213668823},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5458413362503052},{"id":"https://openalex.org/keywords/symmetric-space","display_name":"Symmetric space","score":0.4626947343349457},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44959867000579834},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4228060245513916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.293670117855072},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19023185968399048}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8990775942802429},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.7795878648757935},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.771222710609436},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6819807887077332},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.613868772983551},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5953177213668823},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5458413362503052},{"id":"https://openalex.org/C139941754","wikidata":"https://www.wikidata.org/wiki/Q3058244","display_name":"Symmetric space","level":2,"score":0.4626947343349457},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44959867000579834},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4228060245513916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.293670117855072},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19023185968399048},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/1484","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1484","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r6/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":false,"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:hdl:10068/315061","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/315061","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Y - Progress report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.206.1055","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.206.1055","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.arizona.edu/%7Esavitt/papers/published/symmet-new.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.7010","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.7010","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_7/PDF/v7i1r6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.9199","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.9199","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0002106v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.484","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.484","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-math.mit.edu/~rstan/papers/sympow.ps.gz","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1484","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1484","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r6/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":false,"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/W1582170611.pdf","grobid_xml":"https://content.openalex.org/works/W1582170611.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W59873121","https://openalex.org/W2044248248","https://openalex.org/W2914659449","https://openalex.org/W2992272554","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W4229054622","https://openalex.org/W4283651310","https://openalex.org/W4283803146","https://openalex.org/W4283792424","https://openalex.org/W2074892781","https://openalex.org/W2964348582","https://openalex.org/W2950682154","https://openalex.org/W1884474794","https://openalex.org/W2514034404","https://openalex.org/W2037442308"],"abstract_inverted_index":{"In":[0,55],"this":[1,53],"paper,":[2],"we":[3],"prove":[4],"that":[5],"the":[6,9,14,17,21,66],"dimension":[7],"of":[8,16,20,25,69],"space":[10,68],"span-":[11],"ned":[12],"by":[13,36],"characters":[15,62],"symmetric":[18],"powers":[19],"standard":[22],"$n$-dimensional":[23],"representation":[24],"$S_n$":[26],"is":[27,34],"asymptotic":[28,49],"to":[29,40,50],"$n^2":[30],"/":[31],"2$.":[32],"This":[33],"proved":[35],"using":[37],"generating":[38],"functions":[39,71],"obtain":[41],"formulas":[42],"for":[43,52,57],"upper":[44],"and":[45],"lower":[46],"bounds,":[47],"both":[48],"$n^2/2$,":[51],"dimension.":[54],"particular,":[56],"$n":[58],"\\ge":[59],"7$,":[60],"these":[61],"do":[63],"not":[64],"span":[65],"full":[67],"class":[70],"on":[72],"$S_n$.":[73]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
