{"id":"https://openalex.org/W1749519282","doi":"https://doi.org/10.37236/4955","title":"On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method","display_name":"On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method","publication_year":2015,"publication_date":"2015-03-30","ids":{"openalex":"https://openalex.org/W1749519282","doi":"https://doi.org/10.37236/4955","mag":"1749519282"},"language":"en","primary_location":{"id":"doi:10.37236/4955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p83/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p83/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014239594","display_name":"Zolt\u00e1n L\u00f3r\u00e1nt Nagy","orcid":"https://orcid.org/0000-0003-2062-5668"},"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/I4210134174","display_name":"Montavid Thermodynamic Research Group","ror":"https://ror.org/02s8j2573","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210134174"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Zolt\u00e1n L\u00f3r\u00e1nt Nagy","raw_affiliation_strings":["MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.\r\nsetany 1/C","MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.#R##N#setany 1/C"],"affiliations":[{"raw_affiliation_string":"MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.\r\nsetany 1/C","institution_ids":["https://openalex.org/I106118109","https://openalex.org/I4210134174"]},{"raw_affiliation_string":"MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.#R##N#setany 1/C","institution_ids":["https://openalex.org/I4210134174","https://openalex.org/I106118109"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049283802","display_name":"Bal\u00e1zs Patk\u00f3s","orcid":"https://orcid.org/0000-0002-1651-2487"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bal\u00e1zs Patk\u00f3s","raw_affiliation_strings":["MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.\r\nsetany 1/C, Hungary and Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences","MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.#R##N#setany 1/C, Hungary and Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.\r\nsetany 1/C, Hungary and Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences","institution_ids":[]},{"raw_affiliation_string":"MTA-ELTE Geometric and Algebraic Combinatorics Research Group, H-1117 Budapest, Pazmany P.#R##N#setany 1/C, Hungary and Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5014239594"],"corresponding_institution_ids":["https://openalex.org/I106118109","https://openalex.org/I4210134174"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0497449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","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":0.9955999851226807,"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":0.9955999851226807,"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/T11166","display_name":"Analytic Number Theory Research","score":0.928600013256073,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9111999869346619,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6790500283241272},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6764151453971863},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6631450653076172},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6505790948867798},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5852187275886536},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5675885677337646},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5241335034370422},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35669589042663574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13831263780593872},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11263975501060486},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09273788332939148},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07060641050338745}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6790500283241272},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6764151453971863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6631450653076172},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6505790948867798},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5852187275886536},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5675885677337646},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5241335034370422},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35669589042663574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13831263780593872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11263975501060486},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09273788332939148},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07060641050338745},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/4955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p83/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"},{"id":"pmh:oai:arXiv.org:1501.00648","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1501.00648","pdf_url":"https://arxiv.org/pdf/1501.00648","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:edit.elte.hu:10831/67254","is_oa":true,"landing_page_url":"http://hdl.handle.net/10831/67254","pdf_url":null,"source":{"id":"https://openalex.org/S4306400126","display_name":"ELTE Digital Institutional Repository (EDIT) (E\u00f6tv\u00f6s Lor\u00e1nd University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I106118109","host_organization_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","host_organization_lineage":["https://openalex.org/I106118109"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1501.00648","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1501.00648","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:1749519282","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/4955","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4955","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p83/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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1749519282.pdf","grobid_xml":"https://content.openalex.org/works/W1749519282.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1200701383","https://openalex.org/W1544642706","https://openalex.org/W1686604849","https://openalex.org/W1984324531","https://openalex.org/W1994539900","https://openalex.org/W2002334392","https://openalex.org/W2019935404","https://openalex.org/W2034962669","https://openalex.org/W2036554929","https://openalex.org/W2068795011","https://openalex.org/W2210497805","https://openalex.org/W2303867231","https://openalex.org/W2745175370","https://openalex.org/W2952103174","https://openalex.org/W2952261439","https://openalex.org/W6679094245"],"related_works":["https://openalex.org/W3010556218","https://openalex.org/W2952261439","https://openalex.org/W2989916841","https://openalex.org/W3000503347","https://openalex.org/W2278042759","https://openalex.org/W3167180680","https://openalex.org/W2242573402","https://openalex.org/W2066285430","https://openalex.org/W2963232981","https://openalex.org/W1974173965","https://openalex.org/W3093537952","https://openalex.org/W2788539287","https://openalex.org/W2059272542","https://openalex.org/W2019903106","https://openalex.org/W2948808248","https://openalex.org/W3099080852","https://openalex.org/W3203098167","https://openalex.org/W2617504623","https://openalex.org/W2950088443","https://openalex.org/W1517258173"],"abstract_inverted_index":{"We":[0,73],"study":[1],"the":[2,7,30,61,64],"function":[3],"$M(n,k)$":[4],"which":[5],"denotes":[6],"number":[8],"of":[9,19,32,34,63,69],"maximal":[10],"$k$-uniform":[11],"intersecting":[12],"families":[13],"$\\mathcal{F}\\subseteq":[14],"\\binom{[n]}{k}$.":[15],"Improving":[16],"a":[17,70],"bound":[18,60],"Balogh,":[20],"Das,":[21],"Delcourt,":[22],"Liu":[23],"and":[24,76,81],"Sharifzadeh":[25],"on":[26,51],"$M(n,k)$,":[27],"we":[28],"determine":[29],"order":[31],"magnitude":[33],"$\\log":[35],"M(n,k)$":[36],"by":[37],"proving":[38],"that":[39],"for":[40],"any":[41],"fixed":[42],"$k$,":[43],"$M(n,k)":[44],"=n^{\\Theta(\\binom{2k}{k})}$":[45],"holds.":[46],"Our":[47],"proof":[48],"is":[49,58],"based":[50],"Tuza's":[52],"set":[53,68],"pair":[54],"approach.The":[55],"main":[56],"idea":[57],"to":[59],"size":[62],"largest":[65],"possible":[66],"point":[67],"cross-intersecting":[71],"system.":[72],"also":[74],"introduce":[75],"investigate":[77],"some":[78],"related":[79],"functions":[80],"parameters.":[82]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}