{"id":"https://openalex.org/W2963959819","doi":"https://doi.org/10.37236/565","title":"A $q$-Analogue of some Binomial Coefficient Identities of Y. Sun","display_name":"A $q$-Analogue of some Binomial Coefficient Identities of Y. Sun","publication_year":2011,"publication_date":"2011-03-31","ids":{"openalex":"https://openalex.org/W2963959819","doi":"https://doi.org/10.37236/565","mag":"2963959819"},"language":"en","primary_location":{"id":"doi:10.37236/565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p78/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/v18i1p78/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101428909","display_name":"Victor J. W. Guo","orcid":"https://orcid.org/0000-0002-4153-715X"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Victor J. W. Guo","raw_affiliation_strings":["Department of Mathematics, East China Normal University Shanghai 200062, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East China Normal University Shanghai 200062, People's Republic of China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091756041","display_name":"Dan-Mei Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan-Mei Yang","raw_affiliation_strings":["Department of Mathematics, East China Normal University Shanghai 200062, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East China Normal University Shanghai 200062, People's Republic of China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.39664144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","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":0.9958999752998352,"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":0.9958999752998352,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9876000285148621,"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":0.9663000106811523,"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/binomial-coefficient","display_name":"Binomial coefficient","score":0.7804040312767029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7126901149749756},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5944059491157532},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46852773427963257},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.433524489402771},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20057418942451477}],"concepts":[{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.7804040312767029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7126901149749756},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5944059491157532},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46852773427963257},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.433524489402771},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20057418942451477}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p78/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"}],"best_oa_location":{"id":"doi:10.37236/565","is_oa":true,"landing_page_url":"https://doi.org/10.37236/565","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p78/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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327803","display_name":"Shanghai Rising-Star Program","ror":null},{"id":"https://openalex.org/F4320335766","display_name":"Shanghai Leading Academic Discipline Project","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963959819.pdf","grobid_xml":"https://content.openalex.org/works/W2963959819.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2999372543","https://openalex.org/W2999604533"],"related_works":["https://openalex.org/W2024600207","https://openalex.org/W1587332544","https://openalex.org/W2473415529","https://openalex.org/W2404891737","https://openalex.org/W2079118119","https://openalex.org/W379674649","https://openalex.org/W2613826160","https://openalex.org/W2329936461","https://openalex.org/W2964237408","https://openalex.org/W2143011322"],"abstract_inverted_index":{"We":[0,49],"give":[1],"a":[2],"$q$-analogue":[3],"of":[4,9,54],"some":[5],"binomial":[6],"coefficient":[7],"identities":[8],"Y.":[10],"Sun":[11],"[Electron.":[12],"J.":[13],"Combin.":[14],"17":[15],"(2010),":[16],"#N20]":[17],"as":[18],"follows:":[19],"\\begin{align*}":[20],"\\sum_{k=0}^{\\lfloor":[21,30],"n/2\\rfloor}{m+k\\brack":[22],"k}_{q^2}{m+1\\brack":[23],"n-2k}_{q}":[24],"q^{n-2k\\choose":[25],"2}":[26,35],"&amp;={m+n\\brack":[27],"n}_{q},":[28],"\\\\":[29],"n/4\\rfloor}{m+k\\brack":[31],"k}_{q^4}{m+1\\brack":[32],"n-4k}_{q}":[33],"q^{n-4k\\choose":[34],"&amp;=\\sum_{k=0}^{\\lfloor":[36],"n/2\\rfloor}(-1)^k{m+k\\brack":[37],"k}_{q^2}{m+n-2k\\brack":[38],"n-2k}_{q},":[39],"\\end{align*}":[40],"where":[41],"${n\\brack":[42],"k}_q$":[43],"stands":[44],"for":[45],"the":[46],"$q$-binomial":[47],"coefficient.":[48],"provide":[50],"two":[51],"proofs,":[52],"one":[53],"which":[55],"is":[56],"combinatorial":[57],"via":[58],"partitions.":[59]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
