{"id":"https://openalex.org/W4385631973","doi":"https://doi.org/10.1007/s11083-023-09644-8","title":"Chain-dependent Conditions in Extremal Set Theory","display_name":"Chain-dependent Conditions in Extremal Set Theory","publication_year":2023,"publication_date":"2023-08-07","ids":{"openalex":"https://openalex.org/W4385631973","doi":"https://doi.org/10.1007/s11083-023-09644-8"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-023-09644-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11083-023-09644-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09644-8.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09644-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091227164","display_name":"D\u00e1niel T. Nagy","orcid":"https://orcid.org/0000-0001-6154-7905"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"HUN-REN 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 T. Nagy","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0001-6154-7905","affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108345483","display_name":"K. L. Nagy","orcid":null},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Kartal Nagy","raw_affiliation_strings":["E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091227164"],"corresponding_institution_ids":["https://openalex.org/I127817813"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18837965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"2","first_page":"551","last_page":"559"},"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":0.9495999813079834,"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":0.9495999813079834,"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/algorithm","display_name":"Algorithm","score":0.5868412852287292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.402206152677536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3693031072616577},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3400248885154724}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5868412852287292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.402206152677536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3693031072616577},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3400248885154724}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11083-023-09644-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11083-023-09644-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09644-8.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11083-023-09644-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s11083-023-09644-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09644-8.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1651159268","display_name":null,"funder_award_id":"PD 137779","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G5865157238","display_name":null,"funder_award_id":"FK132060","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"}],"funders":[{"id":"https://openalex.org/F4320322192","display_name":"Magyar Tudom\u00e1nyos Akad\u00e9mia","ror":"https://ror.org/02ks8qq67"},{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385631973.pdf","grobid_xml":"https://content.openalex.org/works/W4385631973.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1989407003","https://openalex.org/W2006708738","https://openalex.org/W2014485295","https://openalex.org/W2072444547","https://openalex.org/W2073286344","https://openalex.org/W2087567316","https://openalex.org/W2963766369","https://openalex.org/W2972668997","https://openalex.org/W3005897571"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"extremal":[2],"set":[3,22],"theory":[4],"our":[5],"usual":[6],"goal":[7],"is":[8,28,33,43,106,127,131],"to":[9,57,70,132],"find":[10],"the":[11,49,115,118,120,138],"maximal":[12],"size":[13,116],"of":[14,17,19,114,117,122],"a":[15,24,36,55,76,134,149],"family":[16,37],"subsets":[18],"an":[20],"n-element":[21],"satisfying":[23],"condition.":[25],"A":[26,88,100],"condition":[27],"called":[29],"chain-dependent,":[30],"if":[31,38,41],"it":[32,42,66,147],"satisfied":[34,44],"for":[35,45],"and":[39,91,145],"only":[40],"its":[46],"intersections":[47],"with":[48,60],"n!":[50],"full":[51,154],"chains.":[52,155],"We":[53],"introduce":[54],"method":[56,130],"handle":[58],"problems":[59,111],"such":[61,84],"conditions,":[62],"then":[63],"show":[64],"how":[65],"can":[67],"be":[68],"used":[69],"prove":[71],"three":[72],"classic":[73],"theorems.":[74],"Then,":[75],"theorem":[77],"about":[78],"families":[79],"containing":[80],"no":[81],"two":[82],"sets":[83,139],"that":[85],"$$A\\subset":[86],"B$$":[87],"\u2282":[89],"B":[90,104],"$$\\lambda":[92],"\\cdot":[93],"|A|":[94],"\\le":[95],"|B|$$":[96],"\u03bb":[97],"\u00b7":[98],"|":[99,101,103,105],"\u2264":[102],"proved.":[107],"Finally,":[108],"we":[109],"investigate":[110],"where":[112],"instead":[113],"family,":[119],"number":[121],"$$\\ell":[123,141],"$$":[124,142],"\u2113":[125,143],"-chains":[126],"maximized.":[128],"Our":[129],"define":[133],"weight":[135],"function":[136],"on":[137],"(or":[140],"-chains)":[144],"use":[146],"in":[148],"double":[150],"counting":[151],"argument":[152],"involving":[153]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
