{"id":"https://openalex.org/W1930520427","doi":"https://doi.org/10.37236/4971","title":"Tokuyama's Identity for Factorial Schur $P$ and $Q$ Functions","display_name":"Tokuyama's Identity for Factorial Schur $P$ and $Q$ Functions","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W1930520427","doi":"https://doi.org/10.37236/4971","mag":"1930520427"},"language":"en","primary_location":{"id":"doi:10.37236/4971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p42/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/v22i2p42/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065150341","display_name":"Ang\u00e8le M. Hamel","orcid":"https://orcid.org/0000-0003-1825-4570"},"institutions":[{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Ang\u00e8le M. Hamel","raw_affiliation_strings":["Wilfrid Laurier University","WIlfrid Laurier University"],"affiliations":[{"raw_affiliation_string":"Wilfrid Laurier University","institution_ids":["https://openalex.org/I75381157"]},{"raw_affiliation_string":"WIlfrid Laurier University","institution_ids":["https://openalex.org/I75381157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083842538","display_name":"Ronald C. King","orcid":"https://orcid.org/0000-0002-9999-6586"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ronald C. King","raw_affiliation_strings":["University of Southampton"],"affiliations":[{"raw_affiliation_string":"University of Southampton","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065150341"],"corresponding_institution_ids":["https://openalex.org/I75381157"],"apc_list":null,"apc_paid":null,"fwci":5.4139,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.95608279,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"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":0.9998999834060669,"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":0.9987000226974487,"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/T11716","display_name":"Random Matrices and Applications","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.8437072038650513},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.7334544658660889},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6582915782928467},{"id":"https://openalex.org/keywords/factorial","display_name":"Factorial","score":0.5771567821502686},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5043963193893433},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5025956630706787},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.44078752398490906},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.43585580587387085},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43043118715286255},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.41089963912963867},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11473500728607178},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10372385382652283},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10229426622390747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06019362807273865}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8437072038650513},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.7334544658660889},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6582915782928467},{"id":"https://openalex.org/C183763347","wikidata":"https://www.wikidata.org/wiki/Q120976","display_name":"Factorial","level":2,"score":0.5771567821502686},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5043963193893433},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5025956630706787},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.44078752398490906},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.43585580587387085},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43043118715286255},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.41089963912963867},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11473500728607178},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10372385382652283},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10229426622390747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06019362807273865},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/4971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p42/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:10.37236/4971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p42/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":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320313602","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05"},{"id":"https://openalex.org/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1930520427.pdf","grobid_xml":"https://content.openalex.org/works/W1930520427.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W24946920","https://openalex.org/W126484231","https://openalex.org/W127121417","https://openalex.org/W171585182","https://openalex.org/W1488554711","https://openalex.org/W1494911820","https://openalex.org/W1556588106","https://openalex.org/W1583867781","https://openalex.org/W1605303195","https://openalex.org/W1625244118","https://openalex.org/W1655270644","https://openalex.org/W1679486839","https://openalex.org/W1816230691","https://openalex.org/W1906775618","https://openalex.org/W1967472879","https://openalex.org/W1968258943","https://openalex.org/W1982288285","https://openalex.org/W1988039240","https://openalex.org/W1999443625","https://openalex.org/W2000697391","https://openalex.org/W2002226076","https://openalex.org/W2004756134","https://openalex.org/W2026897841","https://openalex.org/W2032817839","https://openalex.org/W2046091890","https://openalex.org/W2078172540","https://openalex.org/W2091600172","https://openalex.org/W2134984950","https://openalex.org/W2963061489","https://openalex.org/W2964303426","https://openalex.org/W4394643607","https://openalex.org/W6600075759","https://openalex.org/W6600351849","https://openalex.org/W6600987040","https://openalex.org/W6602000871","https://openalex.org/W6602123778","https://openalex.org/W6602173343","https://openalex.org/W6635100807","https://openalex.org/W6636007523"],"related_works":["https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W4293585078","https://openalex.org/W2389636997","https://openalex.org/W2349018871","https://openalex.org/W2080915594","https://openalex.org/W2135355720","https://openalex.org/W2383889139"],"abstract_inverted_index":{"A":[0],"recent":[1],"paper":[2],"of":[3,12,19,26,39,46,57],"Bump,":[4],"McNamara":[5],"and":[6,30],"Nakasuji":[7],"introduced":[8],"a":[9,27,31],"factorial":[10],"version":[11],"Tokuyama's":[13],"identity,":[14],"expressing":[15],"the":[16,24,44,55],"partition":[17],"function":[18],"six":[20],"vertex":[21],"model":[22],"as":[23],"product":[25],"$t$-deformed":[28],"Vandermonde":[29],"Schur":[32],"function.":[33],"Here":[34],"we":[35],"provide":[36],"an":[37],"extension":[38],"their":[40],"result":[41],"by":[42],"exploiting":[43],"language":[45],"primed":[47],"shifted":[48],"tableaux,":[49],"with":[50],"its":[51],"proof":[52],"based":[53],"on":[54],"use":[56],"non-interesecting":[58],"lattice":[59],"paths.":[60]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}