{"id":"https://openalex.org/W2128425974","doi":"https://doi.org/10.37236/4932","title":"Combinatorics of Tableau Inversions","display_name":"Combinatorics of Tableau Inversions","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W2128425974","doi":"https://doi.org/10.37236/4932","mag":"2128425974"},"language":"en","primary_location":{"id":"doi:10.37236/4932","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4932","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p44/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/v22i2p44/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022496711","display_name":"Jonathan E. Beagley","orcid":"https://orcid.org/0000-0002-3566-3539"},"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":"Jonathan E. Beagley","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"]}]},{"author_position":"last","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":false,"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":2,"corresponding_author_ids":["https://openalex.org/A5022496711"],"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":0.12142857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"2","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9937999844551086,"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":0.9934999942779541,"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":0.9705541133880615},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7690322995185852},{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.652532696723938},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.624887228012085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5818586349487305},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.2517973482608795},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.04692980647087097}],"concepts":[{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.9705541133880615},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7690322995185852},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.652532696723938},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.624887228012085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5818586349487305},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.2517973482608795},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.04692980647087097},{"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/4932","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4932","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p44/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:1412.6473","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.6473","pdf_url":"https://arxiv.org/pdf/1412.6473","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":null},{"id":"mag:2128425974","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1412.6473.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":"pmh:oai:scholar.valpo.edu:mcs_fac_pubs-1023","is_oa":false,"landing_page_url":"http://scholar.valpo.edu/mcs_fac_pubs/24","pdf_url":null,"source":{"id":"https://openalex.org/S4306401623","display_name":"ValpoScholar (Valparaiso University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149744451","host_organization_name":"Valparaiso University","host_organization_lineage":["https://openalex.org/I149744451"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics and Computer Science Faculty Publications","raw_type":"text"},{"id":"doi:10.48550/arxiv.1412.6473","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.6473","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-journal"}],"best_oa_location":{"id":"doi:10.37236/4932","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4932","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p44/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/W2128425974.pdf","grobid_xml":"https://content.openalex.org/works/W2128425974.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2080111445"],"related_works":["https://openalex.org/W2962923432","https://openalex.org/W1862379588","https://openalex.org/W283627692","https://openalex.org/W2963742703","https://openalex.org/W78071767","https://openalex.org/W2128430147","https://openalex.org/W3008661811","https://openalex.org/W2094031059","https://openalex.org/W2949355062","https://openalex.org/W1920209951","https://openalex.org/W2112687189","https://openalex.org/W2912219853","https://openalex.org/W2893806796","https://openalex.org/W2239718764","https://openalex.org/W2162537444","https://openalex.org/W2783289843","https://openalex.org/W1753095122","https://openalex.org/W2963744284","https://openalex.org/W2962881308","https://openalex.org/W3160399941"],"abstract_inverted_index":{"A":[0],"tableau":[1,10,33,37,75,94,122],"inversion":[2,42],"is":[3,34],"a":[4,35,71,78,97,112,125,138,155],"pair":[5],"of":[6,18,56,65,82,93,107,114,137,145,154],"entries":[7],"in":[8,14,59],"row-standard":[9,36],"$T$":[11,19,28],"that":[12,68,123],"lie":[13],"the":[15,22,53,63,83,91,105,152],"same":[16],"column":[17],"yet":[20],"lack":[21],"appropriate":[23],"relative":[24],"ordering":[25],"to":[26,51,70,77,120,159],"make":[27],"column-standard.":[29],"An":[30],"$i$-inverted":[31,66,108,134],"Young":[32,74,109,128,135,143],"along":[38],"with":[39,62,141],"precisely":[40],"$i$":[41],"pairs.":[43],"Tableau":[44],"inversions":[45,95],"were":[46],"originally":[47],"introduced":[48],"by":[49],"Fresse":[50],"calculate":[52,160],"Betti":[54,80],"numbers":[55],"Springer":[57],"fibers":[58],"Type":[60],"A,":[61],"number":[64,81,106],"tableaux":[67,110,115,136,144,161],"standardize":[69,124],"fixed":[72],"standard":[73,127],"corresponding":[76],"specific":[79,126],"associated":[84],"fiber.":[85],"In":[86],"this":[87],"paper":[88],"we":[89,149],"approach":[90],"topic":[92],"from":[96],"completely":[98],"combinatorial":[99],"perspective.":[100],"We":[101],"develop":[102],"formulas":[103],"enumerating":[104],"for":[111],"variety":[113],"shapes,":[116],"not":[117],"restricting":[118],"ourselves":[119],"inverted":[121],"tableau,":[129],"and":[130],"construct":[131],"bijections":[132],"between":[133],"certain":[139],"shape":[140],"$j$-inverted":[142],"different":[146],"shapes.":[147],"Finally,":[148],"share":[150],"some":[151],"results":[153],"computer":[156],"program":[157],"developed":[158],"inversions.":[162]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}