{"id":"https://openalex.org/W7214092180","doi":"https://doi.org/10.48550/arxiv.2609.26607","title":"Erd\u0151s-Ko-Rado properties of Steiner 2-designs","display_name":"Erd\u0151s-Ko-Rado properties of Steiner 2-designs","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214092180","doi":"https://doi.org/10.48550/arxiv.2609.26607"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26607","pdf_url":"https://arxiv.org/pdf/2609.26607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.26607","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031469231","display_name":"Sam Adriaensen","orcid":"https://orcid.org/0000-0002-0925-9305","observed_orcids":["https://orcid.org/0000-0002-0925-9305"]},"institutions":[{"id":"https://openalex.org/I13469542","display_name":"Vrije Universiteit Brussel","ror":"https://ror.org/006e5kg04","country_code":"BE","type":"education","lineage":["https://openalex.org/I13469542"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Adriaensen, Sam","raw_affiliation_strings":["Department of Mathematics and Data Science , Vrije Universiteit Brussel , Brussels , Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Data Science , Vrije Universiteit Brussel , Brussels , Belgium","institution_ids":["https://openalex.org/I13469542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043484233","display_name":"Sergey V. Goryainov","orcid":"https://orcid.org/0000-0003-1016-6517","observed_orcids":["https://orcid.org/0000-0003-1016-6517"]},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Goryainov, Sergey","raw_affiliation_strings":["School of Mathematical Sciences , Hebei International Joint Research Center for Mathematics and Interdisciplinary Science , Hebei Key Laboratory of Computational Mathematics and Applications , Hebei Workstation for Foreign Academicians , Hebei Normal University , Shijiazhuang 050024 , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Hebei International Joint Research Center for Mathematics and Interdisciplinary Science , Hebei Key Laboratory of Computational Mathematics and Applications , Hebei Workstation for Foreign Academicians , Hebei Normal University , Shijiazhuang 050024 , P.R. China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011121243","display_name":"Elena V. Konstantinova","orcid":"https://orcid.org/0000-0002-3457-645X","observed_orcids":["https://orcid.org/0000-0002-3457-645X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konstantinova, Elena V.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006648448","display_name":"Vedran Kr\u010dadinac","orcid":"https://orcid.org/0000-0001-5199-0911","observed_orcids":["https://orcid.org/0000-0001-5199-0911"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kr\u010dadinac, Vedran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9121000170707703,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9121000170707703,"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/T10849","display_name":"Finite Group Theory Research","score":0.05209999904036522,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.019200000911951065,"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/erdos-ko-rado-theorem","display_name":"Erd\u0151s-Ko-Rado theorem","score":0.906000018119812}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7548999786376953},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7504000067710876},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5985000133514404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5008000135421753},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.23409999907016754},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.23330000042915344}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26607","pdf_url":"https://arxiv.org/pdf/2609.26607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.26607","doi":"https://doi.org/10.48550/arxiv.2609.26607","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26607","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.26607","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26607","pdf_url":"https://arxiv.org/pdf/2609.26607","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310928","display_name":"Sveu\u010dili\u0161te u Zagrebu","ror":"https://ror.org/00mv6sv71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336698","display_name":"Overseas Expertise Introduction Center for Discipline Innovation of Food Nutrition and Human Health (111 Center)","ror":null},{"id":"https://openalex.org/F4320337033","display_name":"Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences","ror":"https://ror.org/00shc0s02"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214092180.pdf","grobid_xml":"https://content.openalex.org/works/W7214092180.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W2012670593","https://openalex.org/W2018989615","https://openalex.org/W2019935404","https://openalex.org/W2049433650","https://openalex.org/W2049701599","https://openalex.org/W2063376272","https://openalex.org/W2092375161","https://openalex.org/W2095169408","https://openalex.org/W2197421906","https://openalex.org/W2290756947","https://openalex.org/W3083124347","https://openalex.org/W3209840056","https://openalex.org/W4205545339","https://openalex.org/W4211079126","https://openalex.org/W4254866411","https://openalex.org/W4392947762","https://openalex.org/W4396228934","https://openalex.org/W4416777446","https://openalex.org/W6891933780"],"related_works":["https://openalex.org/W4408131289","https://openalex.org/W4400773492","https://openalex.org/W2474631264","https://openalex.org/W2952836264","https://openalex.org/W2323410012","https://openalex.org/W758373576","https://openalex.org/W2197421906","https://openalex.org/W2063376272","https://openalex.org/W3118754754","https://openalex.org/W1993695643"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,77],"prove":[4],"an":[5],"Erd\u0151s-Ko-Rado":[6],"characterisation":[7],"of":[8,12,27,62,72,82],"maximum":[9,44,91],"intersecting":[10,45,92],"families":[11],"blocks":[13],"in":[14],"Steiner":[15,37],"$2$-designs":[16],"arising":[17],"from":[18],"Desarguesian":[19],"maximal":[20],"arcs.":[21],"This":[22],"answers":[23],"a":[24,43,54,59,70,79],"recent":[25],"question":[26],"Goryainov":[28],"and":[29,31,65,74],"Konstantinova,":[30],"implies":[32],"that,":[33],"among":[34],"the":[35],"known":[36],"$2$-designs,":[38],"only":[39],"finitely":[40],"many":[41],"admit":[42],"family":[46],"that":[47],"is":[48],"neither":[49],"canonical":[50],"nor":[51],"associated":[52],"with":[53,85],"subdesign.":[55],"We":[56],"also":[57],"perform":[58],"computational":[60],"study":[61],"$2$-$(120,8,1)$":[63],"designs":[64,84],"find":[66],"strong":[67],"counterexamples":[68],"to":[69],"problem":[71],"Godsil":[73],"Meagher.":[75],"Finally,":[76],"give":[78],"parametric":[80],"generalisation":[81],"$2$-$(66,6,1)$":[83],"tight":[86],"dual":[87],"arcs":[88],"as":[89],"non-canonical":[90],"families.":[93]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}