{"id":"https://openalex.org/W4400532546","doi":"https://doi.org/10.1007/s00493-024-00115-1","title":"On Pisier Type Theorems","display_name":"On Pisier Type Theorems","publication_year":2024,"publication_date":"2024-07-11","ids":{"openalex":"https://openalex.org/W4400532546","doi":"https://doi.org/10.1007/s00493-024-00115-1"},"language":"lv","primary_location":{"id":"doi:10.1007/s00493-024-00115-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00115-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00115-1.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","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/s00493-024-00115-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070558406","display_name":"Jaroslav Ne\u0161et\u0159il","orcid":"https://orcid.org/0000-0002-5133-5586"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Jaroslav Ne\u0161et\u0159il","raw_affiliation_strings":["Department of applied Mathematics and Institute of Theoretical Computer Science, Charles University, 11800, Praha 1, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of applied Mathematics and Institute of Theoretical Computer Science, Charles University, 11800, Praha 1, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109078443","display_name":"Vojt\u011bch R\u00f6dl","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vojt\u011bch R\u00f6dl","raw_affiliation_strings":["Department of Mathematics, Emory University, Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Emory University, Atlanta, GA, USA","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110947200","display_name":"Marcelo Sales","orcid":null},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marcelo Sales","raw_affiliation_strings":["Department of Mathematics, University of California, Irvine, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110947200"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":1.0711,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.69800885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"44","issue":"6","first_page":"1211","last_page":"1232"},"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":0.9993000030517578,"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":0.9993000030517578,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9916999936103821,"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/mathematics","display_name":"Mathematics","score":0.6617399454116821},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6215709447860718},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4897039234638214},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.42874228954315186},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07718643546104431},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.056275784969329834}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6617399454116821},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6215709447860718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4897039234638214},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.42874228954315186},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07718643546104431},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.056275784969329834}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-024-00115-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00115-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00115-1.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-024-00115-1","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00493-024-00115-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-024-00115-1.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1664930887","display_name":"Extremal and Ramsey-Type Problems for Graphs and Hypergraphs","funder_award_id":"1764385","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G8320375912","display_name":"Collaborative Research: Extremal and Ramsey Problems for Graphs and Hypergraphs","funder_award_id":"2300347","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400532546.pdf","grobid_xml":"https://content.openalex.org/works/W4400532546.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W93222883","https://openalex.org/W1781028155","https://openalex.org/W1965994418","https://openalex.org/W1967245832","https://openalex.org/W1968319543","https://openalex.org/W1975319287","https://openalex.org/W1983132041","https://openalex.org/W1987254493","https://openalex.org/W2005672194","https://openalex.org/W2009160544","https://openalex.org/W2009545408","https://openalex.org/W2320909447"],"related_works":["https://openalex.org/W4387497383","https://openalex.org/W2948807893","https://openalex.org/W2778153218","https://openalex.org/W2748952813","https://openalex.org/W1531601525","https://openalex.org/W4391375266","https://openalex.org/W2078814861","https://openalex.org/W2527526854","https://openalex.org/W1976181487","https://openalex.org/W1986764834"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"any":[2,91],"integer":[3],"$$h\\geqslant":[4,66],"2$$":[5,67],"h":[6,29,44,53,68,88,103,128,155],"\u2a7e":[7,69,113],"2":[8,70],",":[9,118],"a":[10,26,57,73,81,137,145],"set":[11,74,146],"of":[12,59,75,83,139,144],"integers":[13,76],"$$B=\\{b_i\\}_{i\\in":[14],"I}$$":[15],"B":[16,28,87,102,154],"=":[17,125],"{":[18],"b":[19,36,42,171],"i":[20,22,37,43,47,52],"}":[21],"\u2208":[23,169],"I":[24],"is":[25,79],"$$B_h$$":[27,86,101,153],"-set":[30,104],"if":[31],"all":[32,161],"h-sums":[33],"$$b_{i_1}+\\ldots":[34],"+b_{i_h}$$":[35],"1":[38,48],"+":[39,41],"\u2026":[40,50],"with":[45,106,148],"$$i_1<\\ldots":[46],"<":[49,51],"are":[54,173],"distinct.":[55,174],"Answering":[56],"question":[58],"Alon":[60],"and":[61],"Erd\u0151s":[62],"[2],":[63],"for":[64],"every":[65],"we":[71],"construct":[72],"X":[77,98],"which":[78],"not":[80],"union":[82],"finitely":[84],"many":[85],"-sets,":[89],"yet":[90],"finite":[92,162],"subset":[93],"$$Y\\subseteq":[94],"X$$":[95],"Y":[96,116],"\u2286":[97],"contains":[99],"an":[100],"Z":[105,111],"$$|Z|\\geqslant":[107],"\\varepsilon":[108],"|Y|$$":[109],"|":[110,112,115,117],"\u03b5":[114,123,126],"where":[119],"$$\\varepsilon":[120],":=\\varepsilon":[121],"(h)$$":[122],":":[124],"(":[127],")":[129],".":[130],"We":[131],"also":[132],"discuss":[133],"questions":[134],"related":[135],"to":[136],"problem":[138],"Pisier":[140],"about":[141],"the":[142,158],"existence":[143],"A":[147],"similar":[149],"properties":[150],"when":[151],"replacing":[152],"-sets":[156],"by":[157],"requirement":[159],"that":[160],"sums":[163],"$$\\sum":[164],"_{j\\in":[165],"J}b_j$$":[166],"\u2211":[167],"j":[168,172],"J":[170]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}