{"id":"https://openalex.org/W3005073584","doi":"https://doi.org/10.37236/8432","title":"d-Galvin Families","display_name":"d-Galvin Families","publication_year":2020,"publication_date":"2020-02-07","ids":{"openalex":"https://openalex.org/W3005073584","doi":"https://doi.org/10.37236/8432","mag":"3005073584"},"language":"en","primary_location":{"id":"doi:10.37236/8432","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8432","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p36/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p36/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013166918","display_name":"Johan H\u00e5stad","orcid":"https://orcid.org/0000-0002-5379-345X"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I2799509149","display_name":"Khyber Teaching Hospital","ror":"https://ror.org/04xnzxv25","country_code":"PK","type":"healthcare","lineage":["https://openalex.org/I2799509149"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["FR","PK","SE"],"is_corresponding":false,"raw_author_name":"Johan H\u00e5stad","raw_affiliation_strings":["KTH","LaBRI Universit\u00e9 de Bordeaux Bordeaux, France","School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH","institution_ids":["https://openalex.org/I2799509149"]},{"raw_affiliation_string":"LaBRI Universit\u00e9 de Bordeaux Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]},{"raw_affiliation_string":"School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007800519","display_name":"Guillaume Lagarde","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I2799509149","display_name":"Khyber Teaching Hospital","ror":"https://ror.org/04xnzxv25","country_code":"PK","type":"healthcare","lineage":["https://openalex.org/I2799509149"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["FR","PK","SE"],"is_corresponding":false,"raw_author_name":"Guillaume Lagarde","raw_affiliation_strings":["KTH","School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm, Sweden","LaBRI Universit\u00e9 de Bordeaux Bordeaux, France","School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH","institution_ids":["https://openalex.org/I2799509149"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"LaBRI Universit\u00e9 de Bordeaux Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]},{"raw_affiliation_string":"School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047905935","display_name":"Joseph Swernofsky","orcid":null},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I2799509149","display_name":"Khyber Teaching Hospital","ror":"https://ror.org/04xnzxv25","country_code":"PK","type":"healthcare","lineage":["https://openalex.org/I2799509149"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["FR","PK","SE"],"is_corresponding":false,"raw_author_name":"Joseph Swernofsky","raw_affiliation_strings":["KTH","School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm, Sweden","School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden","LaBRI Universit\u00e9 de Bordeaux Bordeaux, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH","institution_ids":["https://openalex.org/I2799509149"]},{"raw_affiliation_string":"School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"School of Engineering Sciences KTH Royal Institute of Technology Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"LaBRI Universit\u00e9 de Bordeaux Bordeaux, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03315169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14395","display_name":"African history and culture studies","score":0.848800003528595,"subfield":{"id":"https://openalex.org/subfields/3314","display_name":"Anthropology"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T14395","display_name":"African history and culture studies","score":0.848800003528595,"subfield":{"id":"https://openalex.org/subfields/3314","display_name":"Anthropology"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.8183000087738037,"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/mathematics","display_name":"Mathematics","score":0.8662573099136353},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7559692859649658},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7503278851509094},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7435222864151001},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.49921345710754395},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.43679261207580566},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4282306134700775},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.40668433904647827},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04647091031074524},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0364585816860199}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8662573099136353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7559692859649658},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7503278851509094},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7435222864151001},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.49921345710754395},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.43679261207580566},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4282306134700775},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.40668433904647827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04647091031074524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0364585816860199},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/8432","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8432","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p36/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"}],"best_oa_location":{"id":"doi:10.37236/8432","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8432","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p36/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":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3005073584.pdf","grobid_xml":"https://content.openalex.org/works/W3005073584.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1569126348","https://openalex.org/W2035175249","https://openalex.org/W2767623943","https://openalex.org/W2928023715","https://openalex.org/W2962756270","https://openalex.org/W2966705569","https://openalex.org/W3009759485","https://openalex.org/W4238472918","https://openalex.org/W4239534271","https://openalex.org/W6643425945"],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W2008149323","https://openalex.org/W2963227734","https://openalex.org/W3127537455","https://openalex.org/W2244330083","https://openalex.org/W2020345516","https://openalex.org/W3099204345","https://openalex.org/W2017219446"],"abstract_inverted_index":{"The":[0],"Galvin":[1],"problem":[2],"asks":[3],"for":[4,20,73],"the":[5,17,67,69,114],"minimum":[6],"size":[7,25,111],"of":[8,24,54,95,110],"a":[9,31,52,60,84,93],"family":[10,85],"$\\mathcal{F}":[11,86],"\\subseteq":[12,87],"\\binom":[13,88],"{[n]}":[14,89],"{n/2}$":[15],"with":[16],"property":[18,71],"that,":[19],"any":[21,74],"set":[22,32],"$A$":[23],"$\\frac":[26],"n":[27],"2$,":[28],"there":[29],"is":[30,37,102],"$S":[33],"\\in":[34],"\\mathcal{F}$":[35],"which":[36],"balanced":[38,103],"on":[39,104],"$A$,":[40,75],"meaning":[41],"that":[42,57,91,99],"$|S":[43],"\\cap":[44,48],"A|":[45],"=":[46],"|S":[47],"\\overline{A}|$.":[49],"We":[50,106],"consider":[51],"generalization":[53,68],"this":[55],"question":[56],"comes":[58],"from":[59,83],"possible":[61],"approach":[62],"in":[63,113],"complexity":[64],"theory.":[65],"In":[66],"required":[70],"is,":[72],"to":[76,79],"be":[77],"able":[78],"find":[80],"$d$":[81],"sets":[82],"{n/d}$":[90],"form":[92],"partition":[94],"$[n]$":[96],"and":[97,117],"such":[98,108],"each":[100],"part":[101],"$A$.":[105],"construct":[107],"families":[109],"polynomial":[112],"parameters":[115],"$n$":[116],"$d$.":[118]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-02-14T00:00:00"}