{"id":"https://openalex.org/W2107514012","doi":"https://doi.org/10.37236/529","title":"The Disjoint $m$-Flower Intersection Problem for Latin Squares","display_name":"The Disjoint $m$-Flower Intersection Problem for Latin Squares","publication_year":2011,"publication_date":"2011-02-21","ids":{"openalex":"https://openalex.org/W2107514012","doi":"https://doi.org/10.37236/529","mag":"2107514012"},"language":"en","primary_location":{"id":"doi:10.37236/529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p42/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/v18i1p42/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029494537","display_name":"James Lefevre","orcid":"https://orcid.org/0000-0002-5945-9575"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"James G. Lefevre","raw_affiliation_strings":["School of Mathematics and Physics, University of Queensland Brisbane, QLD, 4072, Australia","University of Queensland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Queensland Brisbane, QLD, 4072, Australia","institution_ids":["https://openalex.org/I165143802"]},{"raw_affiliation_string":"University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065865197","display_name":"Thomas A. McCourt","orcid":null},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Thomas A. McCourt","raw_affiliation_strings":["School of Mathematics and Physics, University of Queensland Brisbane, QLD, 4072, Australia","University of Queensland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Queensland Brisbane, QLD, 4072, Australia","institution_ids":["https://openalex.org/I165143802"]},{"raw_affiliation_string":"University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5406,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.71802311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"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/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.954800009727478,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9390000104904175,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.9288666248321533},{"id":"https://openalex.org/keywords/latin-square","display_name":"Latin square","score":0.850995659828186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8348414301872253},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8070753216743469},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7347850203514099},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5140355825424194},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.49624568223953247},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.4679108262062073},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4185272455215454},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3514017164707184},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09629020094871521},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.08322831988334656},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07247111201286316}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.9288666248321533},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.850995659828186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8348414301872253},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8070753216743469},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7347850203514099},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5140355825424194},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.49624568223953247},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4679108262062073},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4185272455215454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3514017164707184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09629020094871521},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.08322831988334656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07247111201286316},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C100544194","wikidata":"https://www.wikidata.org/wiki/Q41760","display_name":"Fermentation","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0},{"id":"https://openalex.org/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p42/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:espace.library.uq.edu.au:UQ:706893","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402388","display_name":"Queensland's institutional digital repository (The University of Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165143802","host_organization_name":"The University of Queensland","host_organization_lineage":["https://openalex.org/I165143802"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.37236/529","is_oa":true,"landing_page_url":"https://doi.org/10.37236/529","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p42/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2107514012.pdf","grobid_xml":"https://content.openalex.org/works/W2107514012.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W168302804","https://openalex.org/W804747756","https://openalex.org/W1597636074","https://openalex.org/W1597940416","https://openalex.org/W1993736506","https://openalex.org/W2018441423","https://openalex.org/W2052883575","https://openalex.org/W2059077714","https://openalex.org/W2081394103","https://openalex.org/W2320377306","https://openalex.org/W2611937745","https://openalex.org/W2753229311"],"related_works":["https://openalex.org/W2044829724","https://openalex.org/W2138391391","https://openalex.org/W2154749105","https://openalex.org/W1971174658","https://openalex.org/W3022165933","https://openalex.org/W2052627508","https://openalex.org/W2053428912","https://openalex.org/W2734892631","https://openalex.org/W1509368739","https://openalex.org/W1970142267"],"abstract_inverted_index":{"An":[0],"$m$-flower":[1],"in":[2,57],"a":[3,7,15,18,22,48,71],"latin":[4,58,74],"square":[5],"is":[6],"set":[8],"of":[9,50,73,76,83],"$m$":[10],"entries":[11],"which":[12,26,66],"share":[13,36],"either":[14],"common":[16,19,23,38],"row,":[17,39],"column,":[20],"or":[21,41],"symbol,":[24],"but":[25],"are":[27,32],"otherwise":[28],"distinct.":[29],"Two":[30],"$m$-flowers":[31,56],"disjoint":[33,55,85],"if":[34],"they":[35],"no":[37],"column":[40],"entry.":[42],"In":[43],"this":[44],"paper":[45],"we":[46,62],"give":[47],"solution":[49],"the":[51],"intersection":[52,80],"problem":[53],"for":[54,65],"squares;":[59],"that":[60],"is,":[61],"determine":[63],"precisely":[64],"triples":[67],"$(n,m,x)$":[68],"there":[69],"exists":[70],"pair":[72],"squares":[75],"order":[77],"$n$":[78],"whose":[79],"consists":[81],"exactly":[82],"$x$":[84],"$m$-flowers.":[86]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
