{"id":"https://openalex.org/W2948592123","doi":"https://doi.org/10.37236/8935","title":"A Combinatorial Model for the Decomposition of Multivariate Polynomial Rings as $S_n$-Modules","display_name":"A Combinatorial Model for the Decomposition of Multivariate Polynomial Rings as $S_n$-Modules","publication_year":2020,"publication_date":"2020-08-07","ids":{"openalex":"https://openalex.org/W2948592123","doi":"https://doi.org/10.37236/8935","mag":"2948592123"},"language":"en","primary_location":{"id":"doi:10.37236/8935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p24/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/v27i3p24/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054549002","display_name":"Rosa Orellana","orcid":"https://orcid.org/0000-0002-8562-3615"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Rosa Orellana","raw_affiliation_strings":["Dartmouth College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":null,"display_name":"Michael Zabrocki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Zabrocki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1903,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84527838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"3","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/T11130","display_name":"Coding theory and cryptography","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.7898205518722534},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7692725658416748},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.6968859434127808},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.630998969078064},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6097511053085327},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6073629856109619},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5944167375564575},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.577339231967926},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.44111618399620056},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43879836797714233},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37300044298171997},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060807377099990845},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05187147855758667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7898205518722534},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7692725658416748},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.6968859434127808},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.630998969078064},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6097511053085327},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6073629856109619},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5944167375564575},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.577339231967926},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.44111618399620056},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43879836797714233},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37300044298171997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060807377099990845},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05187147855758667},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p24/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:1906.01125","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1906.01125","pdf_url":"https://arxiv.org/pdf/1906.01125","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":"mag:2948592123","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1906.01125.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1906.01125","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1906.01125","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"}],"best_oa_location":{"id":"doi:10.37236/8935","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8935","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i3p24/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/G2666821625","display_name":null,"funder_award_id":"DMS-1700058","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3626015223","display_name":null,"funder_award_id":"DMS-1300512","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5562185665","display_name":"Combinatorial Representation Theory","funder_award_id":"1300512","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/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2948592123.pdf","grobid_xml":"https://content.openalex.org/works/W2948592123.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1596298884","https://openalex.org/W1634042400","https://openalex.org/W1837462315","https://openalex.org/W1991774414","https://openalex.org/W2006224450","https://openalex.org/W2009754675","https://openalex.org/W2014234764","https://openalex.org/W2037343549","https://openalex.org/W2048519828","https://openalex.org/W2060066939","https://openalex.org/W2061606438","https://openalex.org/W2062555545","https://openalex.org/W2120930689","https://openalex.org/W2134984950","https://openalex.org/W2264201660","https://openalex.org/W2314507527","https://openalex.org/W2315352971","https://openalex.org/W2907379407","https://openalex.org/W2914659449","https://openalex.org/W2916540119","https://openalex.org/W2924983445","https://openalex.org/W3043752321","https://openalex.org/W3100074305","https://openalex.org/W3126072351","https://openalex.org/W3158027121","https://openalex.org/W3189762330","https://openalex.org/W6600020421","https://openalex.org/W6600431890","https://openalex.org/W6634446315","https://openalex.org/W6639345454","https://openalex.org/W6642068429","https://openalex.org/W6659729074","https://openalex.org/W6748249730"],"related_works":["https://openalex.org/W2050626380","https://openalex.org/W1996945520","https://openalex.org/W1643028418","https://openalex.org/W1881128296","https://openalex.org/W2753759351","https://openalex.org/W2962747708","https://openalex.org/W3033740928","https://openalex.org/W2011958701","https://openalex.org/W3011320375","https://openalex.org/W2790473119","https://openalex.org/W2896533482","https://openalex.org/W3128361046","https://openalex.org/W2766399774","https://openalex.org/W2336753305","https://openalex.org/W3082127726","https://openalex.org/W2084482962","https://openalex.org/W2035487874","https://openalex.org/W3186276664","https://openalex.org/W2046154000","https://openalex.org/W3184741431"],"abstract_inverted_index":{"We":[0,57],"consider":[1],"the":[2,7,27,34,42,65],"symmetric":[3],"group":[4],"$S_n$-module":[5],"of":[6,13,20,29,39,44,47,67,71],"polynomial":[8],"ring":[9,66],"with":[10],"$m$":[11],"sets":[12,19],"$n$":[14,21],"commuting":[15],"variables":[16,23],"and":[17,24,53],"$m'$":[18],"anti-commuting":[22],"show":[25],"that":[26],"multiplicity":[28],"an":[30],"irreducible":[31],"indexed":[32],"by":[33],"partition":[35,38],"$\\lambda$":[36,49],"(a":[37],"$n$)":[40],"is":[41],"number":[43],"multiset":[45],"tableaux":[46],"shape":[48],"satisfying":[50],"certain":[51],"column":[52],"row":[54],"strict":[55],"conditions.":[56],"also":[58],"present":[59],"a":[60],"finite":[61],"generating":[62],"set":[63],"for":[64],"$S_n$":[68],"invariant":[69],"polynomials":[70],"this":[72],"ring.":[73]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
