{"id":"https://openalex.org/W4297065913","doi":"https://doi.org/10.37236/10579","title":"The \"Young\" and \"Reverse\" Dichotomy of Polynomials","display_name":"The \"Young\" and \"Reverse\" Dichotomy of Polynomials","publication_year":2022,"publication_date":"2022-09-23","ids":{"openalex":"https://openalex.org/W4297065913","doi":"https://doi.org/10.37236/10579"},"language":"en","primary_location":{"id":"doi:10.37236/10579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p61/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":"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/v29i3p61/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007744325","display_name":"Sarah Mason","orcid":"https://orcid.org/0009-0000-8613-5974"},"institutions":[{"id":"https://openalex.org/I47251452","display_name":"Wake Forest University","ror":"https://ror.org/0207ad724","country_code":"US","type":"education","lineage":["https://openalex.org/I47251452"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sarah Mason","raw_affiliation_strings":["Wake Forest University"],"affiliations":[{"raw_affiliation_string":"Wake Forest University","institution_ids":["https://openalex.org/I47251452"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063906754","display_name":"Dominic Searles","orcid":null},"institutions":[{"id":"https://openalex.org/I80281795","display_name":"University of Otago","ror":"https://ror.org/01jmxt844","country_code":"NZ","type":"education","lineage":["https://openalex.org/I80281795"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Dominic Searles","raw_affiliation_strings":["University of Otago"],"affiliations":[{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007744325"],"corresponding_institution_ids":["https://openalex.org/I47251452"],"apc_list":null,"apc_paid":null,"fwci":0.5568,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60825106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","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":0.9994000196456909,"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":0.9994000196456909,"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":0.9986000061035156,"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/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7701524496078491},{"id":"https://openalex.org/keywords/schur-polynomial","display_name":"Schur polynomial","score":0.6607683897018433},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.5979866981506348},{"id":"https://openalex.org/keywords/hopf-algebra","display_name":"Hopf algebra","score":0.5760103464126587},{"id":"https://openalex.org/keywords/young-tableau","display_name":"Young tableau","score":0.5538031458854675},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5495388507843018},{"id":"https://openalex.org/keywords/involution","display_name":"Involution (esoterism)","score":0.5049026608467102},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.49784374237060547},{"id":"https://openalex.org/keywords/difference-polynomials","display_name":"Difference polynomials","score":0.4555453360080719},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4174138903617859},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36165422201156616},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32016584277153015},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31761783361434937},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.27701491117477417}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7701524496078491},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.6607683897018433},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.5979866981506348},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.5760103464126587},{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.5538031458854675},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5495388507843018},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.5049026608467102},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.49784374237060547},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.4555453360080719},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4174138903617859},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36165422201156616},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32016584277153015},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31761783361434937},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.27701491117477417},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/10579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p61/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"}],"best_oa_location":{"id":"doi:10.37236/10579","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10579","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p61/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4297065913.pdf","grobid_xml":"https://content.openalex.org/works/W4297065913.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W267142216","https://openalex.org/W652863819","https://openalex.org/W1511084141","https://openalex.org/W1518468345","https://openalex.org/W1539091812","https://openalex.org/W1551177513","https://openalex.org/W1974746744","https://openalex.org/W1990770892","https://openalex.org/W1995152055","https://openalex.org/W1995154714","https://openalex.org/W2000642568","https://openalex.org/W2004540213","https://openalex.org/W2037773266","https://openalex.org/W2039041861","https://openalex.org/W2064406668","https://openalex.org/W2075784671","https://openalex.org/W2153901794","https://openalex.org/W2331950050","https://openalex.org/W2417980922","https://openalex.org/W2443570680","https://openalex.org/W2491288446","https://openalex.org/W2520741081","https://openalex.org/W2525947532","https://openalex.org/W2618078593","https://openalex.org/W2726095539","https://openalex.org/W2806526379","https://openalex.org/W2922497929","https://openalex.org/W2949592496","https://openalex.org/W2962696715","https://openalex.org/W2962986001","https://openalex.org/W2963846206","https://openalex.org/W2964311535","https://openalex.org/W2996148054","https://openalex.org/W3104993986","https://openalex.org/W3122983934","https://openalex.org/W3155658708","https://openalex.org/W3167199273","https://openalex.org/W3188941880","https://openalex.org/W4210989028","https://openalex.org/W6643848384","https://openalex.org/W6929189386"],"related_works":["https://openalex.org/W4282813460","https://openalex.org/W1879712717","https://openalex.org/W2282900067","https://openalex.org/W4288555406","https://openalex.org/W2917894457","https://openalex.org/W4300167689","https://openalex.org/W4300180694","https://openalex.org/W4388927664","https://openalex.org/W1504493895","https://openalex.org/W4297065913"],"abstract_inverted_index":{"A":[0],"``flip-and-reversal\"":[1],"involution":[2],"arising":[3],"in":[4,38],"the":[5,39,70,74,81,107,121],"study":[6,40],"of":[7,22,24,41,43,49,59,73,92,110,123],"quasisymmetric":[8,27],"Schur":[9],"functions":[10,83],"provides":[11],"a":[12,89],"passage":[13],"between":[14],"what":[15],"we":[16,53],"term":[17],"``Young\"":[18],"and":[19,47,55,87,126],"``reverse\"":[20],"variants":[21],"bases":[23,61,125],"polynomials":[25,95],"or":[26],"functions.":[28],"Building":[29],"on":[30,98],"this":[31],"perspective,":[32],"which":[33],"has":[34],"found":[35],"recent":[36],"application":[37],"q-analogues":[42],"combinatorial":[44,67,104],"Hopf":[45],"algebras":[46],"generalizations":[48],"dual":[50],"immaculate":[51],"functions,":[52],"develop":[54],"explore":[56],"Young":[57,71,93,108,128],"analogues":[58,109],"well-known":[60],"for":[62,69,84,106],"polynomials.":[63],"We":[64,101,118],"prove":[65],"several":[66],"formulas":[68,105],"analogue":[72],"key":[75,94],"polynomials,":[76,112],"show":[77],"that":[78],"they":[79],"form":[80],"generating":[82],"left":[85],"keys,":[86],"provide":[88],"representation-theoretic":[90],"interpretation":[91],"as":[96],"traces":[97],"certain":[99],"modules.":[100],"also":[102],"give":[103],"Schubert":[111],"including":[113],"their":[114,127,132],"crystal":[115],"graph":[116],"structure.":[117],"moreover":[119],"determine":[120],"intersections":[122],"(reverse)":[124],"counterparts,":[129],"further":[130],"clarifying":[131],"relationships":[133],"to":[134],"one":[135],"another.":[136]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
