{"id":"https://openalex.org/W2623587465","doi":"https://doi.org/10.37236/7073","title":"Forbidden Subposet Problems for Traces of Set Families","display_name":"Forbidden Subposet Problems for Traces of Set Families","publication_year":2018,"publication_date":"2018-09-21","ids":{"openalex":"https://openalex.org/W2623587465","doi":"https://doi.org/10.37236/7073","mag":"2623587465"},"language":"en","primary_location":{"id":"doi:10.37236/7073","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7073","pdf_url":null,"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://doi.org/10.37236/7073","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071291505","display_name":"D\u00e1niel Gerbner","orcid":"https://orcid.org/0000-0001-7080-2883"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"D\u00e1niel Gerbner","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049283802","display_name":"Bal\u00e1zs Patk\u00f3s","orcid":"https://orcid.org/0000-0002-1651-2487"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Bal\u00e1zs Patk\u00f3s","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018834142","display_name":"M\u00e1t\u00e9 Vizer","orcid":"https://orcid.org/0000-0002-2360-3918"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"funder","lineage":["https://openalex.org/I7597260"]},{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"M\u00e1t\u00e9 Vizer","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\r\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics,\nHungarian Academy of Sciences","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071291505"],"corresponding_institution_ids":["https://openalex.org/I127817813","https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":1.6136,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.78554932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","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":0.9746000170707703,"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":0.9746000170707703,"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":0.859849214553833},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.8060030341148376},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7773171663284302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7486380934715271},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6474913358688354},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5537419319152832},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5489516854286194},{"id":"https://openalex.org/keywords/family-of-sets","display_name":"Family of sets","score":0.4624401032924652},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.35757893323898315},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3492487668991089}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.859849214553833},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.8060030341148376},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7773171663284302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7486380934715271},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6474913358688354},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5537419319152832},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5489516854286194},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.4624401032924652},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35757893323898315},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3492487668991089},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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:10.37236/7073","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7073","pdf_url":null,"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:10.37236/7073","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7073","pdf_url":null,"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":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2054008041","https://openalex.org/W2952295216","https://openalex.org/W4299355653","https://openalex.org/W802045817","https://openalex.org/W2952419066","https://openalex.org/W2022700105","https://openalex.org/W4300764115","https://openalex.org/W2950253054","https://openalex.org/W2891088981","https://openalex.org/W4313597867"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,119],"introduce":[4,78],"a":[5,20,23,29,66,70,157],"problem":[6],"that":[7,35],"bridges":[8],"forbidden":[9,12,167],"subposet":[10,168],"and":[11,98,140],"subconfiguration":[13],"problems.":[14,169],"The":[15,63],"sets":[16,51],"$F_1,F_2,":[17],"\\dots,F_{|P|}$":[18],"form":[19],"copy":[21,60],"of":[22,50,61,65,116,124,144,148,159,163,166],"poset":[24,133],"$P$,":[25],"if":[26,54,87,103],"there":[27],"exists":[28],"bijection":[30],"$i:P\\rightarrow":[31],"\\{F_1,F_2,":[32],"\\dots,F_{|P|}\\}$":[33],"such":[34],"for":[36,88,108,152],"any":[37,59,89],"$p,p'\\in":[38],"P$":[39],"the":[40,79,93,113,121,131,142,145,160,164],"relation":[41],"$p<_P":[42],"p'$":[43],"implies":[44],"$i(p)\\subsetneq":[45],"i(p')$.":[46],"A":[47],"family":[48,67,94],"$\\mathcal{F}$":[49,68,99],"is":[52,73,84,96,100,105,130],"$P$-free":[53,86,97,102,107],"it":[55,104],"does":[56],"not":[57],"contain":[58],"$P$.":[62],"trace":[64,101,125],"on":[69,134],"set":[71],"$X$":[72],"$\\mathcal{F}|_X:=\\{F\\cap":[74],"X:":[75],"F\\in":[76],"\\mathcal{F}\\}$.We":[77],"following":[80],"notions:":[81],"$\\mathcal{F}\\subseteq":[82],"2^{[n]}$":[83],"$l$-trace":[85,106],"$l$-subset":[90],"$L\\subseteq":[91],"[n]$,":[92],"$\\mathcal{F}|_L$":[95],"all":[109],"$l\\le":[110],"n$.":[111],"As":[112],"first":[114],"instances":[115],"these":[117],"problems":[118],"determine":[120,141],"maximum":[122,146],"size":[123,147],"$B$-free":[126],"families,":[127],"where":[128],"$B$":[129],"butterfly":[132],"four":[135],"elements":[136],"$a,b,c,d$":[137],"with":[138],"$a,b<c,d$":[139],"asymptotics":[143],"$(n-i)$-trace":[149],"$K_{r,s}$-free":[150],"families":[151],"$i=1,2$.":[153],"We":[154],"also":[155],"propose":[156],"generalization":[158],"main":[161],"conjecture":[162],"area":[165]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}