{"id":"https://openalex.org/W2611969982","doi":"https://doi.org/10.37236/6970","title":"Tail Positive Words and Generalized Coinvariant Algebras","display_name":"Tail Positive Words and Generalized Coinvariant Algebras","publication_year":2017,"publication_date":"2017-07-28","ids":{"openalex":"https://openalex.org/W2611969982","doi":"https://doi.org/10.37236/6970","mag":"2611969982"},"language":"en","primary_location":{"id":"doi:10.37236/6970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6970","pdf_url":null,"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://doi.org/10.37236/6970","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016834944","display_name":"Brendon Rhoades","orcid":"https://orcid.org/0000-0003-0433-5185"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brendon Rhoades","raw_affiliation_strings":["University of California, San Diego","University of California\u2014San Diego"],"affiliations":[{"raw_affiliation_string":"University of California, San Diego","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California\u2014San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014375002","display_name":"Andrew Timothy Wilson","orcid":"https://orcid.org/0000-0003-1325-2867"},"institutions":[{"id":"https://openalex.org/I36788626","display_name":"California University of Pennsylvania","ror":"https://ror.org/01spssf70","country_code":"US","type":"education","lineage":["https://openalex.org/I36788626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Timothy Wilson","raw_affiliation_strings":["University of Pennsylvania","#N#               * University of Pennsylvania"],"affiliations":[{"raw_affiliation_string":"University of Pennsylvania","institution_ids":["https://openalex.org/I36788626"]},{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016834944"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":1.19143819,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7041067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"24","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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7794331908226013},{"id":"https://openalex.org/keywords/hecke-algebra","display_name":"Hecke algebra","score":0.7649730443954468},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7151567339897156},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7133426666259766},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6746184825897217},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.581885576248169},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.5529282689094543},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5418558716773987},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4694468677043915},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4661831557750702},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4544728696346283},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44400909543037415},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.43970224261283875},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3120773732662201},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.30596235394477844},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.06855207681655884}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7794331908226013},{"id":"https://openalex.org/C2781280181","wikidata":"https://www.wikidata.org/wiki/Q48970267","display_name":"Hecke algebra","level":3,"score":0.7649730443954468},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7151567339897156},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7133426666259766},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6746184825897217},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.581885576248169},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.5529282689094543},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5418558716773987},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4694468677043915},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4661831557750702},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4544728696346283},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44400909543037415},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.43970224261283875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3120773732662201},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30596235394477844},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.06855207681655884},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/6970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6970","pdf_url":null,"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:1704.02618","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1704.02618","pdf_url":"https://arxiv.org/pdf/1704.02618","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1704.02618","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1704.02618","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"},{"id":"mag:2611969982","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:10.37236/6970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6970","pdf_url":null,"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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2042843318","https://openalex.org/W2052510964","https://openalex.org/W2077039617","https://openalex.org/W2150030676","https://openalex.org/W2157675040","https://openalex.org/W2525947532","https://openalex.org/W2582351923","https://openalex.org/W2793886524","https://openalex.org/W3099698207"],"related_works":["https://openalex.org/W2963105949","https://openalex.org/W2785174575","https://openalex.org/W2793886524","https://openalex.org/W2072313319","https://openalex.org/W2981171146","https://openalex.org/W3208119519","https://openalex.org/W2034432275","https://openalex.org/W2087522574","https://openalex.org/W1528722892","https://openalex.org/W2049863239","https://openalex.org/W2963869706","https://openalex.org/W2962789810","https://openalex.org/W2952679828","https://openalex.org/W2952649720","https://openalex.org/W2047772280","https://openalex.org/W1594105856","https://openalex.org/W2962977651","https://openalex.org/W3159127186","https://openalex.org/W2797670632","https://openalex.org/W2604612980"],"abstract_inverted_index":{"Let":[0],"$n,k,$":[1],"and":[2,7,98,123,127,139],"$r$":[3],"be":[4,10],"nonnegative":[5],"integers":[6],"let":[8],"$S_n$":[9],"the":[11,20,31,45,50,57,75,82,92,111,140,144],"symmetric":[12,58],"group.":[13,59],"We":[14,90,103,131],"introduce":[15],"a":[16,34,108,119,133],"quotient":[17,46,137],"$R_{n,k,r}$":[18,47,78,97,106,117,138],"of":[19,33,64,71,77,84,96,143,146],"polynomial":[21],"ring":[22],"$\\mathbb{Q}[x_1,":[23],"\\dots,":[24],"x_n]$":[25],"in":[26,73],"$n$":[27],"variables":[28],"which":[29],"carries":[30],"structure":[32],"graded":[35,100],"$S_n$-module.":[36],"When":[37],"$r":[38],"\\ge":[39],"n$":[40],"or":[41],"$k":[42],"=":[43],"0$":[44],"reduces":[48],"to":[49,56],"classical":[51],"coinvariant":[52],"algebra":[53,76,113],"$R_n$":[54,65],"attached":[55],"Just":[60],"as":[61,107],"algebraic":[62],"properties":[63,70],"are":[66],"controlled":[67,80],"by":[68,81],"combinatorial":[69],"permutations":[72],"$S_n$,":[74],"is":[79,118],"combinatorics":[83],"objects":[85],"called":[86],"tail":[87],"positive":[88],"words.":[89],"calculate":[91,124],"standard":[93],"monomial":[94],"basis":[95],"its":[99,125],"$S_n$-isomorphism":[101],"type.":[102],"also":[104],"view":[105],"module":[109],"over":[110],"0-Hecke":[112,121,129],"$H_n(0)$,":[114],"prove":[115],"that":[116],"projective":[120],"module,":[122],"quasisymmetric":[126],"nonsymmetric":[128],"characteristics.":[130],"conjecture":[132],"relationship":[134],"between":[135],"our":[136],"delta":[141],"operators":[142],"theory":[145],"Macdonald":[147],"polynomials.":[148]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
