{"id":"https://openalex.org/W4251019256","doi":"https://doi.org/10.37236/1575","title":"Towards a Katona Type Proof for the 2-intersecting Erd\u0151s-Ko-Rado Theorem","display_name":"Towards a Katona Type Proof for the 2-intersecting Erd\u0151s-Ko-Rado Theorem","publication_year":2001,"publication_date":"2001-10-09","ids":{"openalex":"https://openalex.org/W4251019256","doi":"https://doi.org/10.37236/1575"},"language":"en","primary_location":{"id":"doi:10.37236/1575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r31/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/v8i1r31/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109925672","display_name":"Ralph W. Howard","orcid":"https://orcid.org/0000-0003-1011-9884"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Ralph Howard","raw_affiliation_strings":["Department of Mathematics, University of South Carolina Columbia, SC 29208, USA","Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of South Carolina Columbia, SC 29208, USA","institution_ids":["https://openalex.org/I155781252"]},{"raw_affiliation_string":"Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102818025","display_name":"Gyula K\u00e1rolyi","orcid":"https://orcid.org/0000-0002-6711-7866"},"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/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["HU","US"],"is_corresponding":false,"raw_author_name":"Gyula K\u00e1rolyi","raw_affiliation_strings":["Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary","Department of Mathematics, University of South Carolina Columbia, SC 29208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina Columbia, SC 29208, USA","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103035080","display_name":"\u0141\u00e1szl\u00f3 A. Sz\u00e9kely","orcid":"https://orcid.org/0000-0002-9470-9111"},"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/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["HU","US"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 A. Sz\u00e9kely","raw_affiliation_strings":["Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary","Department of Mathematics, University of South Carolina Columbia, SC 29208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Algebra and Number Theory, E\u00f6tv\u00f6s University 1518 Budapest, Pf. 120, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Department of Mathematics, University of South Carolina Columbia, SC 29208, USA","institution_ids":["https://openalex.org/I155781252"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109925672"],"corresponding_institution_ids":["https://openalex.org/I106118109","https://openalex.org/I155781252"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.41337386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","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":0.9958000183105469,"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":0.9958000183105469,"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":0.9422000050544739,"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/T14094","display_name":"Italy: Economic History and Contemporary Issues","score":0.9273999929428101,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.882260799407959},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.7123834490776062},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6201901435852051},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5371381044387817},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.498013973236084},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.4240756332874298},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.046505868434906006}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.882260799407959},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.7123834490776062},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6201901435852051},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5371381044387817},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.498013973236084},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.4240756332874298},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.046505868434906006},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.37236/1575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r31/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.110.2634","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.2634","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~szekely/twoint9constr.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.21.9382","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.9382","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PDF/v8i1r31.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.6972","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.6972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_8/PostScriptfiles/v8i1r31.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.5298","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.5298","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~szekely/twoint9constr.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.35.1742","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.1742","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~howard/Reprints/katona.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.4120","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.4120","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.sc.edu/~howard/Reprints/katona.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1575","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1575","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r31/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":[{"id":"https://openalex.org/G2811237814","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321994","display_name":"Hungarian Scientific Research Fund","ror":"https://ror.org/00v349e63"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4251019256.pdf","grobid_xml":"https://content.openalex.org/works/W4251019256.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1583642092","https://openalex.org/W1966494790","https://openalex.org/W1972392483","https://openalex.org/W1987233725","https://openalex.org/W1992844673","https://openalex.org/W2006943297","https://openalex.org/W2010763265","https://openalex.org/W2019935404","https://openalex.org/W2092058985","https://openalex.org/W2118426850","https://openalex.org/W2155567071","https://openalex.org/W4298414065"],"related_works":["https://openalex.org/W4299386009","https://openalex.org/W3153156984","https://openalex.org/W2980963558","https://openalex.org/W2949404826","https://openalex.org/W4312107268","https://openalex.org/W2012995322","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2059650901","https://openalex.org/W4301376359"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,5,13,44],"possibility":[3],"of":[4,7,21,52],"existence":[6],"a":[8,33],"Katona":[9],"type":[10,25],"proof":[11],"for":[12,16,27,49],"Erd\u0151s-Ko-Rado":[14,24],"theorem":[15,26],"2-":[17],"and":[18,32,54],"3-intersecting":[19],"families":[20],"sets.":[22],"An":[23],"2-intersecting":[28,45],"integer":[29],"arithmetic":[30],"progressions":[31],"model":[34],"theoretic":[35],"argument":[36],"show":[37],"that":[38],"such":[39],"an":[40],"approach":[41],"works":[42],"in":[43],"case,":[46],"at":[47],"least":[48],"some":[50],"values":[51],"$n$":[53],"$k$.":[55]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
