{"id":"https://openalex.org/W2216073622","doi":"https://doi.org/10.1112/jlms/jdw067","title":"The maximum product of weights of cross-intersecting families","display_name":"The maximum product of weights of cross-intersecting families","publication_year":2016,"publication_date":"2016-11-07","ids":{"openalex":"https://openalex.org/W2216073622","doi":"https://doi.org/10.1112/jlms/jdw067","mag":"2216073622"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdw067","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdw067","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1512.09108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038574319","display_name":"Peter Borg","orcid":"https://orcid.org/0000-0002-9668-3453"},"institutions":[{"id":"https://openalex.org/I197854408","display_name":"University of Malta","ror":"https://ror.org/03a62bv60","country_code":"MT","type":"education","lineage":["https://openalex.org/I197854408"]}],"countries":["MT"],"is_corresponding":true,"raw_author_name":"Peter Borg","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, University of Malta, Msida MSD 2080, Malta","Univ. of Malta#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, University of Malta, Msida MSD 2080, Malta","institution_ids":["https://openalex.org/I197854408"]},{"raw_affiliation_string":"Univ. of Malta#TAB#","institution_ids":["https://openalex.org/I197854408"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038574319"],"corresponding_institution_ids":["https://openalex.org/I197854408"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":1.3812,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77049976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"94","issue":"3","first_page":"993","last_page":"1018"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9984999895095825,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9240999817848206,"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/T10849","display_name":"Finite Group Theory Research","score":0.9133999943733215,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8318480253219604},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5937182903289795},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5426178574562073},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.47822779417037964},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.47391805052757263},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.24585798382759094},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10941770672798157}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8318480253219604},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5937182903289795},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5426178574562073},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.47822779417037964},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.47391805052757263},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.24585798382759094},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10941770672798157},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1112/jlms/jdw067","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdw067","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1512.09108","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.09108","pdf_url":"https://arxiv.org/pdf/1512.09108","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2216073622","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1512.09108.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:open-archive.highwire.org:jlms:94/3/993","is_oa":false,"landing_page_url":"http://jlms.oxfordjournals.org/cgi/content/short/94/3/993","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"TEXT"},{"id":"doi:10.48550/arxiv.1512.09108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.09108","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1512.09108","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.09108","pdf_url":"https://arxiv.org/pdf/1512.09108","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2216073622.pdf","grobid_xml":"https://content.openalex.org/works/W2216073622.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W153370943","https://openalex.org/W1482165026","https://openalex.org/W1503526018","https://openalex.org/W1533352408","https://openalex.org/W1534511119","https://openalex.org/W1559562756","https://openalex.org/W1612837658","https://openalex.org/W1969693428","https://openalex.org/W1977358838","https://openalex.org/W1978573479","https://openalex.org/W1980803848","https://openalex.org/W1987233725","https://openalex.org/W1988856559","https://openalex.org/W1992472342","https://openalex.org/W1995238527","https://openalex.org/W1995680324","https://openalex.org/W1998914526","https://openalex.org/W2000600113","https://openalex.org/W2006901918","https://openalex.org/W2012908763","https://openalex.org/W2019935404","https://openalex.org/W2024552814","https://openalex.org/W2025324955","https://openalex.org/W2031983827","https://openalex.org/W2034494703","https://openalex.org/W2040624880","https://openalex.org/W2041062057","https://openalex.org/W2041346411","https://openalex.org/W2052422078","https://openalex.org/W2056842939","https://openalex.org/W2065647202","https://openalex.org/W2069619900","https://openalex.org/W2074954099","https://openalex.org/W2079135110","https://openalex.org/W2083241416","https://openalex.org/W2090246161","https://openalex.org/W2093718341","https://openalex.org/W2102524299","https://openalex.org/W2103137300","https://openalex.org/W2105006061","https://openalex.org/W2139398905","https://openalex.org/W2169853232","https://openalex.org/W2237599464","https://openalex.org/W2395767617","https://openalex.org/W2477351027","https://openalex.org/W2516050763","https://openalex.org/W2963311461","https://openalex.org/W3000480331","https://openalex.org/W3099904847","https://openalex.org/W3101420482","https://openalex.org/W3136243343","https://openalex.org/W3143189643","https://openalex.org/W6632048837","https://openalex.org/W6721096331","https://openalex.org/W6730370666"],"related_works":["https://openalex.org/W2963485039","https://openalex.org/W2553914555","https://openalex.org/W3115928073","https://openalex.org/W2801724022","https://openalex.org/W2849745612","https://openalex.org/W3103512505","https://openalex.org/W2084293435","https://openalex.org/W1837479661","https://openalex.org/W2949103818","https://openalex.org/W3024996095","https://openalex.org/W2201806318","https://openalex.org/W2763824976","https://openalex.org/W2962791685","https://openalex.org/W2075524965","https://openalex.org/W2040624880","https://openalex.org/W3038113379","https://openalex.org/W1971363122","https://openalex.org/W1978573479","https://openalex.org/W2236355028","https://openalex.org/W3098671307"],"abstract_inverted_index":{"A":[0,10,23,205,222,230,232,235,277,326],"set":[1,21,26,39,75],"of":[2,47,49,53,73,78,120,123,138,140,160,307,319,321,391,397],"sets":[3,161],"is":[4,41,339,380],"called":[5],"a":[6,54,66,74,79,299],"family.":[7,56],"Two":[8],"families":[9,325,390,396],"and":[11,84,128,188,221,223,273,285,303,332,394,410],"B":[12,28,213,224,238,240,243,286,333],"are":[13,199,225],"said":[14],"to":[15,42,88,313,382],"be":[16,117,135,157],"cross-":[17,50,67,226,323,407],"t-intersecting":[18,51,324,408],"if":[19,177,276],"each":[20,25],"in":[22,27,29,37,162,298],"intersects":[24],"at":[30,146],"least":[31],"t":[32,156,171,254,267,284,293,342,345,348,351,367,378],"elements.":[33,149],"An":[34],"active":[35],"problem":[36],"extremal":[38],"theory":[40],"determine":[43],"the":[44,59,86,118,136,158,305,311,316],"maximum":[45,317],"product":[46,318],"sizes":[48,320],"subfamilies":[52],"given":[55],"This":[57],"incorporates":[58],"classical":[60],"Erd\u00f6s\u2013Ko\u2013Rado":[61],"(EKR)":[62],"problem.":[63],"We":[64,174,295,309,385],"prove":[65,296],"t-intersection":[68],"theorem":[69],"for":[70,91,352,389,395,403],"weighted":[71],"subsets":[72,122,139],"by":[76],"means":[77],"new":[80],"subfamily":[81],"alteration":[82],"method,":[83],"use":[85,310],"result":[87,312],"provide":[89],"solutions":[90],"three":[92],"natural":[93],"families.":[94],"For":[95],"r":[96,116,134,148,154,167,184,211,252,282,331,343,363,374],"\u2208":[97,231,239,248,261],"[":[98,113,124,130,141,163,170,180,191,207,215,328,335],"n":[99,109,114,125,131,142,152,164,192,216,263,289,336,346,357,360,371],"]":[100,115,126,132,143,165,172,182,193,209,217,330,337],"=":[101,278,287],"{":[102,354],"1":[103],",":[104,106,108,111,127,153,155,212,220,251,253,264,266,272,281,283,290,292,356,364,366,369,375,377],"2":[105,406],"...":[107],"}":[110,358],"let":[112,129],"family":[119,137,159],"r-element":[121],"\u2264":[133,166,183,194,210,218,245],"that":[144,168,176,201,315],"have":[145],"most":[147],"Let":[150],"F":[151,249,262,279,288],"contain":[169],".":[173,294],"show":[175,314],"g":[178,233,255],":":[179,190],"m":[181,208,250,280,329,340,355],"\u2192":[185,196],"R":[186,197],"+":[187,198],"h":[189,241,268],"s":[195,219,265,291,338,349,365,376],"functions":[200],"obey":[202],"certain":[203],"conditions,":[204],"\u2286":[206,214,327,334],"t-intersecting,":[227],"then":[228],"\u2211":[229,237,246,259],"(":[234,242,256,269,362,373],")":[236,244,258,271,368,379],"C":[247,257],"D":[260,270],"equality":[274],"holds":[275],"this":[297],"more":[300],"general":[301],"setting":[302],"characterize":[304],"cases":[306],"equality.":[308],"two":[322],"-":[341,344,347,350],"min":[353],"\u2a7e":[359,405],"0":[361,372],"where":[370],"close":[381],"best":[383],"possible.":[384],"obtain":[386],"analogous":[387],"results":[388,400],"integer":[392],"sequences":[393],"multisets.":[398],"The":[399],"yield":[401],"generalizations":[402],"k":[404],"families,":[409],"EKR-type":[411],"results.":[412]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}