{"id":"https://openalex.org/W2111159105","doi":"https://doi.org/10.37236/1625","title":"Set-Systems with Restricted Multiple Intersections","display_name":"Set-Systems with Restricted Multiple Intersections","publication_year":2002,"publication_date":"2002-02-20","ids":{"openalex":"https://openalex.org/W2111159105","doi":"https://doi.org/10.37236/1625","mag":"2111159105"},"language":"en","primary_location":{"id":"doi:10.37236/1625","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1625","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r8/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r8/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052560792","display_name":"Vince Grolmusz","orcid":"https://orcid.org/0000-0001-9456-8876"},"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"]},{"id":"https://openalex.org/I4210161853","display_name":"Budapest Institute","ror":"https://ror.org/050hvq478","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210161853"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Vince Grolmusz","raw_affiliation_strings":["Department of Computer Science Etvs University, H-1117 Budapest HUNGARY","Department of Computer Science E\u00f6tv\u00f6s University, H-1117 Budapest HUNGARY"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Etvs University, H-1117 Budapest HUNGARY","institution_ids":["https://openalex.org/I4210161853"]},{"raw_affiliation_string":"Department of Computer Science E\u00f6tv\u00f6s University, H-1117 Budapest HUNGARY","institution_ids":["https://openalex.org/I106118109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052560792"],"corresponding_institution_ids":["https://openalex.org/I106118109","https://openalex.org/I4210161853"],"apc_list":null,"apc_paid":null,"fwci":2.2254,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87528868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/combinatorics","display_name":"Combinatorics","score":0.8808979988098145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8805774450302124},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.8180595636367798},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.767747163772583},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6015018820762634},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.5598834753036499},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5136777758598328},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4234082102775574}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8808979988098145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8805774450302124},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.8180595636367798},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.767747163772583},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6015018820762634},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.5598834753036499},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5136777758598328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4234082102775574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1625","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1625","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r8/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":false,"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":null,"license_id":null,"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:10.37236/1625","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1625","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r8/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":false,"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":null,"license_id":null,"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/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2111159105.pdf","grobid_xml":"https://content.openalex.org/works/W2111159105.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1268512041","https://openalex.org/W1898703922","https://openalex.org/W2017023281","https://openalex.org/W2039991502","https://openalex.org/W2054996571","https://openalex.org/W2064197162","https://openalex.org/W2069582894","https://openalex.org/W2090746613","https://openalex.org/W2798428635","https://openalex.org/W3119119221","https://openalex.org/W4237031071","https://openalex.org/W6654512821"],"related_works":["https://openalex.org/W2509614667","https://openalex.org/W4376608589","https://openalex.org/W2963293152","https://openalex.org/W4302199713","https://openalex.org/W4282026465","https://openalex.org/W3138003926","https://openalex.org/W4300037846","https://openalex.org/W1630514295","https://openalex.org/W1537073411","https://openalex.org/W2963081352"],"abstract_inverted_index":{"We":[0],"give":[1,92],"a":[2,22,38,82,93],"generalization":[3],"for":[4,27,97],"the":[5,30,42,45,57,99],"Deza-Frankl-Singhi":[6],"Theorem":[7],"in":[8,52],"case":[9],"of":[10,44,47,59,74,84,101],"multiple":[11],"intersections.":[12],"More":[13],"exactly,":[14],"we":[15,91],"prove,":[16],"that":[17,26,110],"if":[18],"${\\cal":[19,48,60],"H}$":[20,49,61],"is":[21,62],"set-system,":[23],"which":[24],"satisfies":[25],"some":[28],"$k$,":[29],"$k$-wise":[31],"intersections":[32],"occupy":[33],"only":[34],"$\\ell$":[35],"residue-classes":[36],"modulo":[37],"$p$":[39],"prime,":[40],"while":[41],"sizes":[43],"members":[46],"are":[50],"not":[51],"these":[53],"residue":[54],"classes,":[55],"then":[56],"size":[58],"at":[63],"most":[64],"$$(k-1)\\sum_{i=0}^{\\ell}{n\\choose":[65],"i}$$":[66],"This":[67],"result":[68],"considerably":[69],"strengthens":[70],"an":[71,89,102],"upper":[72],"bound":[73],"F\u00fcredi":[75],"(1983),":[76],"and":[77],"gives":[78],"partial":[79],"answer":[80],"to":[81],"question":[83],"T.":[85],"S\u00f3s":[86],"(1976).":[87],"As":[88],"application,":[90],"direct,":[94],"explicit":[95],"construction":[96],"coloring":[98],"$k$-subsets":[100],"$n$":[103],"element":[104],"set":[105],"with":[106],"$t$":[107],"colors,":[108],"such":[109],"no":[111],"monochromatic":[112],"complete":[113],"hypergraph":[114],"on":[115],"$$\\exp{(c(\\log":[116],"m)^{1/t}(\\log":[117],"\\log":[118],"m)^{1/(t-1)})}$$":[119],"vertices":[120],"exists.":[121]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
