{"id":"https://openalex.org/W7214044840","doi":"https://doi.org/10.48550/arxiv.2609.23584","title":"The existence spectrum of near triple arrays with four rows","display_name":"The existence spectrum of near triple arrays with four rows","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214044840","doi":"https://doi.org/10.48550/arxiv.2609.23584"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23584","pdf_url":"https://arxiv.org/pdf/2609.23584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.23584","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152483838","display_name":"GuangZhou Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, GuangZhou","raw_affiliation_strings":[". School of Mathematics and Statistics , Henan Normal University , Xinxiang , 453007 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Mathematics and Statistics , Henan Normal University , Xinxiang , 453007 , P. R. China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152484558","display_name":"Yaxin Yue","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue, Yaxin","raw_affiliation_strings":[". School of Mathematics and Statistics , Henan Normal University , Xinxiang , 453007 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Mathematics and Statistics , Henan Normal University , Xinxiang , 453007 , P. R. China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159939249","display_name":"Yong Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210141689","display_name":"Yancheng Teachers University","ror":"https://ror.org/042k5fe81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210141689"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Yong","raw_affiliation_strings":[". School of Mathematics and Statistics , Yancheng Teachers University , Yancheng 224002 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Mathematics and Statistics , Yancheng Teachers University , Yancheng 224002 , P. R. China","institution_ids":["https://openalex.org/I4210141689"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.8633000254631042,"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":0.8633000254631042,"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/T10849","display_name":"Finite Group Theory Research","score":0.050700001418590546,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.04100000113248825,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/experimental-design","display_name":"experimental design","score":0.5550000071525574},{"id":"https://openalex.org/keywords/intersection-property","display_name":"intersection property","score":0.6940000057220459},{"id":"https://openalex.org/keywords/replication-number","display_name":"replication number","score":0.9729999899864197},{"id":"https://openalex.org/keywords/combinatorial-designs","display_name":"combinatorial designs","score":0.777999997138977}],"concepts":[{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.7178000211715698},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.67330002784729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6272000074386597},{"id":"https://openalex.org/C2778282194","wikidata":"https://www.wikidata.org/wiki/Q1199041","display_name":"Triple junction","level":2,"score":0.6040999889373779},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5367000102996826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4697999954223633},{"id":"https://openalex.org/C26979961","wikidata":"https://www.wikidata.org/wiki/Q36248","display_name":"Triple product","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.3871999979019165},{"id":"https://openalex.org/C109385661","wikidata":"https://www.wikidata.org/wiki/Q11358307","display_name":"Triple system","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C58070368","wikidata":"https://www.wikidata.org/wiki/Q106410","display_name":"Triple point","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C2775882903","wikidata":"https://www.wikidata.org/wiki/Q7843496","display_name":"Triple arthrodesis","level":4,"score":0.34779998660087585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3264000117778778},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32010000944137573},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.29809999465942383},{"id":"https://openalex.org/C10919887","wikidata":"https://www.wikidata.org/wiki/Q7843514","display_name":"Triple helix","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C196099240","wikidata":"https://www.wikidata.org/wiki/Q177033","display_name":"Triple bond","level":3,"score":0.27970001101493835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27720001339912415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23584","pdf_url":"https://arxiv.org/pdf/2609.23584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.23584","doi":"https://doi.org/10.48550/arxiv.2609.23584","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23584","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23584","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23584","pdf_url":"https://arxiv.org/pdf/2609.23584","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4637761775","display_name":null,"funder_award_id":"262300421846","funder_id":"https://openalex.org/F4320323845","funder_display_name":"Natural Science Foundation of Henan Province"},{"id":"https://openalex.org/G8423293363","display_name":null,"funder_award_id":"12471245","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214044840.pdf","grobid_xml":"https://content.openalex.org/works/W7214044840.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7170138627"],"related_works":["https://openalex.org/W6979253360","https://openalex.org/W1988860354","https://openalex.org/W7114784242","https://openalex.org/W2082971190","https://openalex.org/W2151570307","https://openalex.org/W1967042059","https://openalex.org/W2980272928","https://openalex.org/W2934859526","https://openalex.org/W2626924018","https://openalex.org/W2511029155"],"abstract_inverted_index":{"In":[0,86],"the":[1,41,52,58,92],"1950s":[2],"and":[3,21,77,101,112],"1960s,":[4],"Agrawal":[5],"introduced":[6],"a":[7,71,106],"class":[8],"of":[9,33,60,94],"experimental":[10],"designs":[11],"that":[12,68,103],"later":[13],"became":[14],"known":[15],"as":[16,45,47],"triple":[17,25,34,62,74,96,109],"arrays.":[18],"Gordeev,":[19],"Markstr\u00f6m":[20],"\u00d6hman":[22],"proposed":[23],"near":[24,61,95],"arrays":[26,63,97],"by":[27],"relaxing":[28],"all":[29],"three":[30,65],"intersection":[31,43],"properties":[32],"arrays,":[35],"allowing":[36],"two":[37,48],"values":[38,50],"concentrated":[39],"around":[40],"average":[42],"size,":[44],"well":[46],"consecutive":[49],"for":[51,84,119],"replication":[53],"numbers.":[54],"They":[55],"completely":[56],"resolved":[57],"existence":[59,93],"with":[64,98],"rows,":[66],"showing":[67],"there":[69,104],"exists":[70,105],"$(3\\times":[72],"c,v)$-near":[73,108],"array":[75,110],"if":[76,79,111,114],"only":[78,113],"$v\\geq":[80,115],"c\\geq":[81,116],"3$":[82],"except":[83,118],"$(c,v)\\in\\{(3,6),(4,6),(5,8)\\}$.":[85],"this":[87],"paper,":[88],"we":[89],"further":[90],"investigate":[91],"four":[99],"rows":[100],"prove":[102],"$(4\\times":[107],"4$":[117],"$(c,v)\\in\\{":[120],"(4,9),(5,7),(5,10),(6,8),(7,9),(10,12),(11,13)\\}$.":[121]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}