{"id":"https://openalex.org/W1862379588","doi":"https://doi.org/10.37236/5469","title":"Inversions of Semistandard Young Tableaux","display_name":"Inversions of Semistandard Young Tableaux","publication_year":2016,"publication_date":"2016-03-04","ids":{"openalex":"https://openalex.org/W1862379588","doi":"https://doi.org/10.37236/5469","mag":"1862379588"},"language":"en","primary_location":{"id":"doi:10.37236/5469","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5469","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p43/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/v23i1p43/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063691222","display_name":"Paul Drube","orcid":null},"institutions":[{"id":"https://openalex.org/I149744451","display_name":"Valparaiso University","ror":"https://ror.org/01pp0fx48","country_code":"US","type":"education","lineage":["https://openalex.org/I149744451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Drube","raw_affiliation_strings":["Valparaiso University","Valpara\u00edso University"],"affiliations":[{"raw_affiliation_string":"Valparaiso University","institution_ids":["https://openalex.org/I149744451"]},{"raw_affiliation_string":"Valpara\u00edso University","institution_ids":["https://openalex.org/I149744451"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063691222"],"corresponding_institution_ids":["https://openalex.org/I149744451"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01683,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","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":0.9976000189781189,"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":0.9976000189781189,"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":0.9912999868392944,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9901999831199646,"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/young-tableau","display_name":"Young tableau","score":0.987693727016449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7697696685791016},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.6533395051956177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6311413049697876},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6018191576004028},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5944565534591675},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.5554933547973633},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.43990007042884827},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.4231416583061218},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.27157437801361084},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14797082543373108},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11415278911590576},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08196902275085449},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05148401856422424}],"concepts":[{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.987693727016449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7697696685791016},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6533395051956177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6311413049697876},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6018191576004028},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5944565534591675},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5554933547973633},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.43990007042884827},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.4231416583061218},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.27157437801361084},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14797082543373108},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11415278911590576},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08196902275085449},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05148401856422424},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/5469","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5469","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p43/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:1508.01175","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.01175","pdf_url":"https://arxiv.org/pdf/1508.01175","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":"mag:1862379588","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1508.01175v1","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.1508.01175","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1508.01175","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:10.37236/5469","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5469","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p43/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":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1862379588.pdf"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1524394135","https://openalex.org/W2080111445","https://openalex.org/W2962923432"],"related_works":["https://openalex.org/W2964055078","https://openalex.org/W2962923432","https://openalex.org/W2963742703","https://openalex.org/W283627692","https://openalex.org/W2149129024","https://openalex.org/W2128430147","https://openalex.org/W78071767","https://openalex.org/W1965521120","https://openalex.org/W2094031059","https://openalex.org/W2112687189","https://openalex.org/W2893806796","https://openalex.org/W2912219853","https://openalex.org/W1920209951","https://openalex.org/W2949355062","https://openalex.org/W2783289843","https://openalex.org/W2170972105","https://openalex.org/W2963236291","https://openalex.org/W2963319824","https://openalex.org/W3138388487","https://openalex.org/W2483763284"],"abstract_inverted_index":{"A":[0],"tableau":[1,15,25,30,34,94,131],"inversion":[2,38,126],"is":[3,31,150],"a":[4,13,32,45,118,129,133,147,163,180,190],"pair":[5],"of":[6,12,47,67,93,107,125,143,146,154,165,179,189,192],"entries":[7,57],"from":[8],"the":[9,18,24,64,122,141],"same":[10],"column":[11],"row-standard":[14,33,97,130],"that":[16,54,140,174],"lack":[17,55],"relative":[19],"ordering":[20],"necessary":[21],"to":[22,62,96,111],"make":[23],"column-standard.":[26],"An":[27],"$i$-inverted":[28,144,159],"Young":[29,49,52,114,160,177,187],"with":[35,99,132,185],"precisely":[36],"$i$":[37],"pairs,":[39],"and":[40,73,86,136,138,167,169],"may":[41],"be":[42],"interpreted":[43],"as":[44,77],"generalization":[46,106],"(column-standard)":[48],"tableaux.":[50,115],"Inverted":[51],"tableaux":[53,98,145,161,178,188],"repeated":[56,100],"were":[58,74],"introduced":[59],"by":[60,84],"Fresse":[61],"calculate":[63],"Betti":[65],"numbers":[66,124],"Springer":[68],"fibers":[69],"in":[70,80,183],"Type":[71],"A,":[72],"later":[75],"developed":[76],"combinatorial":[78],"objects":[79],"their":[81],"own":[82],"right":[83],"Beagley":[85],"Drube.":[87],"This":[88],"paper":[89],"generalizes":[90],"earlier":[91,172],"notions":[92],"inversions":[95],"entries,":[101],"yielding":[102],"an":[103,171],"interesting":[104],"new":[105],"semistandard":[108],"(as":[109],"opposed":[110],"merely":[112],"standard)":[113],"We":[116,156],"develop":[117],"closed":[119],"formula":[120],"for":[121,128,162],"maximum":[123],"pairs":[127],"specific":[134],"shape":[135,149,182],"content,":[137],"show":[139],"number":[142],"given":[148],"invariant":[151],"under":[152],"permutation":[153],"content.":[155],"then":[157],"enumerate":[158],"variety":[164,191],"shapes":[166],"contents,":[168],"generalize":[170],"result":[173],"places":[175],"$1$-inverted":[176],"general":[181],"bijection":[184],"$0$-inverted":[186],"related":[193],"shapes.":[194]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
