{"id":"https://openalex.org/W2999237617","doi":"https://doi.org/10.37236/1985","title":"The Intersection Structure of $t$-Intersecting Families","display_name":"The Intersection Structure of $t$-Intersecting Families","publication_year":2005,"publication_date":"2005-10-13","ids":{"openalex":"https://openalex.org/W2999237617","doi":"https://doi.org/10.37236/1985","mag":"2999237617"},"language":"en","primary_location":{"id":"doi:10.37236/1985","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1985","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n18/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/v12i1n18/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002343159","display_name":"John Talbot","orcid":"https://orcid.org/0000-0002-4119-9429"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"John Talbot","raw_affiliation_strings":["Department of Mathematics University College London, London, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University College London, London, UK","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002343159"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3526245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"1","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9916999936103821,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9810000061988831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8590085506439209},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8413521647453308},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.742631733417511},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.7189199924468994},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7105932235717773},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5907589197158813},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5071337223052979},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41556090116500854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38253557682037354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0534747838973999}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8590085506439209},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8413521647453308},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.742631733417511},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.7189199924468994},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7105932235717773},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5907589197158813},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5071337223052979},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41556090116500854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38253557682037354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0534747838973999},{"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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1985","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1985","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n18/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:10.37236/1985","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1985","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n18/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999237617.pdf","grobid_xml":"https://content.openalex.org/works/W2999237617.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1569752386","https://openalex.org/W1964432727","https://openalex.org/W1993616423","https://openalex.org/W1994539900","https://openalex.org/W2016341899","https://openalex.org/W2019935404","https://openalex.org/W4298414065"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2194570607"],"abstract_inverted_index":{"A":[0],"family":[1,12,22],"of":[2,23,32,40,65],"sets":[3,9,31],"is":[4],"$t$-intersecting":[5,21],"if":[6],"any":[7],"two":[8],"from":[10,25],"the":[11,66],"contain":[13],"at":[14],"least":[15],"$t$":[16],"common":[17],"elements.":[18],"Given":[19],"a":[20,63],"$r$-sets":[24],"an":[26,45],"$n$-set,":[27],"how":[28],"many":[29],"distinct":[30],"size":[33],"$k$":[34],"can":[35,53,59],"occur":[36],"as":[37,62],"pairwise":[38],"intersections":[39],"its":[41],"members?":[42],"We":[43],"prove":[44],"asymptotic":[46],"upper":[47],"bound":[48],"on":[49],"this":[50],"number":[51],"that":[52],"always":[54],"be":[55,60],"achieved.":[56],"This":[57],"result":[58],"seen":[61],"generalization":[64],"Erd\u0151s-Ko-Rado":[67],"theorem.":[68]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}