{"id":"https://openalex.org/W4210542080","doi":"https://doi.org/10.37236/10121","title":"Union-Closed Families with Small Average Overlap Densities","display_name":"Union-Closed Families with Small Average Overlap Densities","publication_year":2022,"publication_date":"2022-01-28","ids":{"openalex":"https://openalex.org/W4210542080","doi":"https://doi.org/10.37236/10121"},"language":"en","primary_location":{"id":"doi:10.37236/10121","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10121","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p11/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p11/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084401924","display_name":"David Ellis","orcid":"https://orcid.org/0000-0001-7149-9521"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"David Ellis","raw_affiliation_strings":["University of Bristol"],"affiliations":[{"raw_affiliation_string":"University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084401924"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09948542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","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":0.9947999715805054,"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":0.9947999715805054,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9205999970436096,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8925046920776367},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8069573640823364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32704925537109375}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8925046920776367},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8069573640823364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32704925537109375}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10121","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10121","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p11/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/18d79451-82e6-4f39-b9ab-a7ab83ef6b01","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/18d79451-82e6-4f39-b9ab-a7ab83ef6b01","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ellis, D 2022, 'Union-closed families with small average overlap densities', Electronic Journal of Combinatorics, vol. 29, no. 1. https://doi.org/10.37236/10121","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2012.03235","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.03235","pdf_url":"https://arxiv.org/pdf/2012.03235","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":"","raw_type":null},{"id":"pmh:oai:research-information.bris.ac.uk:publications/18d79451-82e6-4f39-b9ab-a7ab83ef6b01","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/18d79451-82e6-4f39-b9ab-a7ab83ef6b01","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ellis, D 2022, 'Union-closed families with small average overlap densities', Electronic Journal of Combinatorics, vol. 29, no. 1. https://doi.org/10.37236/10121","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.37236/10121","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10121","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p11/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/W4210542080.pdf","grobid_xml":"https://content.openalex.org/works/W4210542080.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W254586386","https://openalex.org/W1621400550","https://openalex.org/W1633614532","https://openalex.org/W2071911955","https://openalex.org/W4293572802","https://openalex.org/W4293863060"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"In":[0],"this":[1],"very":[2],"short":[3],"paper,":[4],"we":[5],"show":[6],"that":[7],"the":[8],"average":[9],"overlap":[10],"density":[11],"of":[12,17,19],"a":[13],"union-closed":[14],"family":[15],"$\\mathcal{F}$":[16],"subsets":[18],"$\\{1,2,\\ldots,n\\}$":[20],"may":[21],"be":[22],"as":[23,25],"small":[24],"\\[\\Theta((\\log_2":[26],"\\log_2":[27],"|\\mathcal{F}|)/(\\log_2":[28],"|\\mathcal{F}|)),\\]":[29],"for":[30],"infinitely":[31],"many":[32],"positive":[33],"integers":[34],"$n$.":[35]},"counts_by_year":[],"updated_date":"2026-03-16T09:10:04.655348","created_date":"2025-10-10T00:00:00"}