{"id":"https://openalex.org/W2185705959","doi":"https://doi.org/10.37236/5749","title":"New Conjectures for Union-Closed Families","display_name":"New Conjectures for Union-Closed Families","publication_year":2016,"publication_date":"2016-08-05","ids":{"openalex":"https://openalex.org/W2185705959","doi":"https://doi.org/10.37236/5749","mag":"2185705959"},"language":"en","primary_location":{"id":"doi:10.37236/5749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p23/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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p23/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070329454","display_name":"Jonad Pulaj","orcid":"https://orcid.org/0000-0002-5741-7187"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jonad Pulaj","raw_affiliation_strings":["Zuse Institute Berlin","Zuse Institute Berlin,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zuse Institute Berlin","institution_ids":["https://openalex.org/I195893171"]},{"raw_affiliation_string":"Zuse Institute Berlin,#TAB#","institution_ids":["https://openalex.org/I195893171"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075797239","display_name":"Annie Raymond","orcid":"https://orcid.org/0000-0002-3577-7624"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Annie Raymond","raw_affiliation_strings":["University of Washington","University of Washington ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington ;","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070611630","display_name":"Dirk Oliver Theis","orcid":"https://orcid.org/0000-0002-9362-0748"},"institutions":[{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE"],"is_corresponding":false,"raw_author_name":"Dirk Theis","raw_affiliation_strings":["University of Tartu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tartu","institution_ids":["https://openalex.org/I56085075"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5823,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59952607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"3","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":0.9986000061035156,"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":0.9986000061035156,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9965999722480774,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8841710090637207},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.8224809169769287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7571337223052979},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6984399557113647},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6825559735298157},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.5981455445289612},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5667998790740967},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5274439454078674},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47544145584106445},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4457092881202698},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4235725998878479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10959228873252869},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.10385766625404358},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09962242841720581},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07247412204742432}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8841710090637207},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.8224809169769287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7571337223052979},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6984399557113647},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6825559735298157},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.5981455445289612},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5667998790740967},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5274439454078674},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47544145584106445},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4457092881202698},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4235725998878479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10959228873252869},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.10385766625404358},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09962242841720581},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07247412204742432},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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":4,"locations":[{"id":"doi:10.37236/5749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p23/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:arXiv.org:1512.00083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.00083","pdf_url":"https://arxiv.org/pdf/1512.00083","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":"text"},{"id":"mag:2185705959","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1512.00083.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":"doi:10.48550/arxiv.1512.00083","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.00083","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":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/5749","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5749","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p23/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2185705959.pdf","grobid_xml":"https://content.openalex.org/works/W2185705959.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W69315576","https://openalex.org/W87992627","https://openalex.org/W96307653","https://openalex.org/W107440705","https://openalex.org/W1502009249","https://openalex.org/W1594599366","https://openalex.org/W1621400550","https://openalex.org/W1633614532","https://openalex.org/W1969964326","https://openalex.org/W1979442039","https://openalex.org/W1993810789","https://openalex.org/W1998292651","https://openalex.org/W2000069550","https://openalex.org/W2010561843","https://openalex.org/W2013467167","https://openalex.org/W2016273509","https://openalex.org/W2016384349","https://openalex.org/W2022700105","https://openalex.org/W2027636325","https://openalex.org/W2047963661","https://openalex.org/W2058431214","https://openalex.org/W2071911955","https://openalex.org/W2072336136","https://openalex.org/W2114722286","https://openalex.org/W2172048044","https://openalex.org/W2265864037","https://openalex.org/W2290137281","https://openalex.org/W2405465658","https://openalex.org/W2950728075","https://openalex.org/W2953242485","https://openalex.org/W3103079811","https://openalex.org/W6650131370","https://openalex.org/W6668468428","https://openalex.org/W6696864909","https://openalex.org/W6833666809"],"related_works":["https://openalex.org/W2964271663","https://openalex.org/W2038662421","https://openalex.org/W3103079811","https://openalex.org/W2016273509","https://openalex.org/W254586386","https://openalex.org/W2962967942","https://openalex.org/W2889235929","https://openalex.org/W1526159769","https://openalex.org/W3144076478","https://openalex.org/W2979106393","https://openalex.org/W2963826084","https://openalex.org/W2112422744","https://openalex.org/W2110313351","https://openalex.org/W2798878397","https://openalex.org/W2102130396","https://openalex.org/W3196314919","https://openalex.org/W2964229558","https://openalex.org/W3211924274","https://openalex.org/W1890114378","https://openalex.org/W2343633133"],"abstract_inverted_index":{"The":[0],"Frankl":[1,142],"conjecture,":[2,9],"also":[3],"known":[4],"as":[5,111,131],"the":[6,27,46,79,85,117,141,158],"union-closed":[7,16,52,92],"sets":[8,49,69,83,96],"states":[10],"that":[11,39,78,116,135],"in":[12,22,50,65,89],"any":[13,105],"finite":[14],"non-empty":[15],"family,":[17],"there":[18],"exists":[19],"an":[20,30,42],"element":[21,63,88],"at":[23,66,101],"least":[24,102],"half":[25],"of":[26,33,48,58,82,157],"sets.":[28],"From":[29],"optimization":[31],"point":[32],"view,":[34],"one":[35,75],"could":[36,76],"instead":[37],"prove":[38,77,154],"$2a$":[40],"is":[41,64,100],"upper":[43],"bound":[44],"to":[45,140,165],"number":[47,81],"a":[51,55,90],"family":[53,93],"on":[54],"ground":[56],"set":[57],"$n$":[59,98],"elements":[60,99],"where":[61],"each":[62],"most":[67,86],"$a$":[68],"for":[70,104],"all":[71],"$a,n\\in":[72],"\\mathbb{N}^+$.":[73,107],"Similarly,":[74],"minimum":[80],"containing":[84],"frequent":[87],"(non-empty)":[91],"with":[94,125],"$m$":[95],"and":[97,133,161],"$\\frac{m}{2}$":[103],"$m,n\\in":[106],"Formulating":[108],"these":[109,129],"problems":[110],"integer":[112],"programs,":[113],"we":[114,120,153],"observe":[115],"optimal":[118],"values":[119],"computed":[121],"do":[122],"not":[123,138],"vary":[124],"$n$.":[126],"We":[127],"formalize":[128],"observations":[130],"conjectures,":[132],"show":[134],"they":[136],"are":[137],"equivalent":[139],"conjecture":[143],"while":[144],"still":[145],"having":[146],"wide-reaching":[147],"implications":[148],"if":[149],"proven":[150],"true.":[151],"Finally,":[152],"special":[155],"cases":[156],"new":[159],"conjectures":[160],"discuss":[162],"possible":[163],"approaches":[164],"solve":[166],"them":[167],"completely.":[168]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
