{"id":"https://openalex.org/W2422684466","doi":"https://doi.org/10.37236/6376","title":"Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers","display_name":"Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers","publication_year":2017,"publication_date":"2017-05-19","ids":{"openalex":"https://openalex.org/W2422684466","doi":"https://doi.org/10.37236/6376","mag":"2422684466"},"language":"en","primary_location":{"id":"doi:10.37236/6376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6376","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/10.37236/6376","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"],"affiliations":[{"raw_affiliation_string":"Valparaiso 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":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05431093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9930999875068665,"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/young-tableau","display_name":"Young tableau","score":0.8549156188964844},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7945139408111572},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7534961700439453},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5452724695205688},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.45924901962280273},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44411128759384155},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34639275074005127},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08540484309196472}],"concepts":[{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.8549156188964844},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7945139408111572},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7534961700439453},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5452724695205688},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.45924901962280273},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44411128759384155},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34639275074005127},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08540484309196472},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/6376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6376","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:1606.04869","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.04869","pdf_url":"https://arxiv.org/pdf/1606.04869","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:2422684466","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1606.04869.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.1606.04869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1606.04869","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:10.37236/6376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6376","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1553824818","https://openalex.org/W2068045918","https://openalex.org/W2796082150","https://openalex.org/W2962923432"],"related_works":["https://openalex.org/W2963742703","https://openalex.org/W1862379588","https://openalex.org/W2128425974","https://openalex.org/W801522318","https://openalex.org/W2079244978","https://openalex.org/W2952880614","https://openalex.org/W2149129024","https://openalex.org/W1570370881","https://openalex.org/W3095172423","https://openalex.org/W283627692","https://openalex.org/W2979785272","https://openalex.org/W1965521120","https://openalex.org/W2094031059","https://openalex.org/W2140640925","https://openalex.org/W2128430147","https://openalex.org/W78071767","https://openalex.org/W2950606837","https://openalex.org/W1884808438","https://openalex.org/W2747880719","https://openalex.org/W3138388487"],"abstract_inverted_index":{"An":[0,73],"inverted":[1],"semistandard":[2,41,63,84,92,171],"Young":[3,42,64,85,93,109,172,190],"tableau":[4,8,21,29],"is":[5,22,35,77,114],"a":[6,11,28,39,90,148],"row-standard":[7],"along":[9],"with":[10,30,174,192],"collection":[12],"of":[13,61,66,82,106,111,124,131,142,155],"inversion":[14,33],"pairs":[15,34],"that":[16,87,151],"quantify":[17],"how":[18],"far":[19],"the":[20,51,59,80,103,129,139,156],"from":[23],"being":[24],"column":[25],"semistandard.":[26],"Such":[27],"precisely":[31],"$k$":[32],"said":[36],"to":[37,89,121,133,166],"be":[38],"$k$-inverted":[40,62,83,107,170,188],"tableau.":[43,94],"Building":[44],"upon":[45],"earlier":[46],"work":[47],"by":[48,117],"Fresse":[49],"and":[50,70,99,127,177],"author,":[52],"this":[53,146],"paper":[54],"develops":[55],"generating":[56,75,149],"functions":[57],"for":[58,79],"numbers":[60,130],"tableaux":[65,86,110,120,173,191],"various":[67,161],"shapes":[68,97],"$\\lambda$":[69,98,113],"contents":[71],"$\\mu$.":[72],"easily-calculable":[74],"function":[76,150],"given":[78],"number":[81,105],"\"standardize\"":[88],"fixed":[91],"For":[95],"$m$-row":[96],"standard":[100,108,189],"content":[101,176],"$\\mu$,":[102],"total":[104],"shape":[112,179,194],"then":[115,164],"enumerated":[116],"relating":[118],"such":[119],"$m$-dimensional":[122,153],"generalizations":[123],"Dyck":[125],"paths":[126],"counting":[128],"\"returns":[132],"ground\"":[134],"in":[135],"those":[136],"paths.":[137],"In":[138],"rectangular":[140],"specialization":[141],"$\\lambda":[143,180],"=":[144,181],"n^m$":[145],"yields":[147],"involves":[152],"analogues":[154],"famed":[157],"Ballot":[158],"numbers.":[159],"Our":[160],"results":[162],"are":[163],"used":[165],"directly":[167],"enumerate":[168],"all":[169,187],"arbitrary":[175],"two-row":[178],"a^1":[182],"b^1$,":[183],"as":[184,186],"well":[185],"two-column":[193],"$\\lambda=2^n$.":[195]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
