{"id":"https://openalex.org/W2126141473","doi":"https://doi.org/10.37236/1078","title":"Two Finite Forms of Watson's Quintuple Product Identity and Matrix Inversion","display_name":"Two Finite Forms of Watson's Quintuple Product Identity and Matrix Inversion","publication_year":2006,"publication_date":"2006-06-12","ids":{"openalex":"https://openalex.org/W2126141473","doi":"https://doi.org/10.37236/1078","mag":"2126141473"},"language":"en","primary_location":{"id":"doi:10.37236/1078","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1078","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r52/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":null,"license_id":null,"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/v13i1r52/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101784967","display_name":"Xiaonan Ma","orcid":"https://orcid.org/0000-0001-8960-7623"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"X. Ma","raw_affiliation_strings":["Department of Mathematics SuZhou University, SuZhou 215006, P.R.China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics SuZhou University, SuZhou 215006, P.R.China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101784967"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22620482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9997000098228455,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9983999729156494,"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/T12504","display_name":"Mathematics and Applications","score":0.9952999949455261,"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/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.8718575239181519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8345829844474792},{"id":"https://openalex.org/keywords/watson","display_name":"Watson","score":0.7413967251777649},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6908440589904785},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6183015704154968},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5284497737884521},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4652223587036133},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45921608805656433},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4114207625389099},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40886810421943665},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12298533320426941},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09698760509490967},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06726175546646118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05478072166442871}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.8718575239181519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8345829844474792},{"id":"https://openalex.org/C2776608531","wikidata":"https://www.wikidata.org/wiki/Q12253","display_name":"Watson","level":2,"score":0.7413967251777649},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6908440589904785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6183015704154968},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5284497737884521},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4652223587036133},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45921608805656433},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4114207625389099},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40886810421943665},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12298533320426941},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09698760509490967},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06726175546646118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05478072166442871},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"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},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1078","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1078","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r52/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.4540","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.4540","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r52.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1078","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1078","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r52/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2126141473.pdf","grobid_xml":"https://content.openalex.org/works/W2126141473.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W610831910","https://openalex.org/W1541544182","https://openalex.org/W1867865005","https://openalex.org/W1971123899","https://openalex.org/W2008052995","https://openalex.org/W2040047002","https://openalex.org/W2053839652","https://openalex.org/W2090058365","https://openalex.org/W4237567533"],"related_works":["https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W3174693904","https://openalex.org/W2902037120","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W2798280117","https://openalex.org/W2094012085","https://openalex.org/W2382399004","https://openalex.org/W2502309190"],"abstract_inverted_index":{"Recently,":[0],"Chen-Chu-Gu":[1],"and":[2],"Guo-Zeng":[3],"found":[4],"independently":[5],"that":[6,30],"Watson's":[7,22],"quintuple":[8,23],"product":[9,24],"identity":[10],"follows":[11],"surprisingly":[12],"from":[13],"two":[14,36],"basic":[15],"algebraic":[16],"identities,":[17],"called":[18],"finite":[19],"forms":[20],"of":[21,39],"identity.":[25],"The":[26],"present":[27],"paper":[28],"shows":[29],"both":[31],"identities":[32],"are":[33],"equivalent":[34],"to":[35],"special":[37],"cases":[38],"the":[40,45],"$q$-Chu-Vandermonde":[41],"formula":[42],"by":[43],"using":[44],"($f,g$)-inversion.":[46]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}