{"id":"https://openalex.org/W4410144728","doi":"https://doi.org/10.1007/s00373-025-02922-9","title":"Set Systems with Covering Properties and Low VC-Dimension","display_name":"Set Systems with Covering Properties and Low VC-Dimension","publication_year":2025,"publication_date":"2025-05-07","ids":{"openalex":"https://openalex.org/W4410144728","doi":"https://doi.org/10.1007/s00373-025-02922-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-02922-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02922-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02922-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","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/s00373-025-02922-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093784772","display_name":"George Peterzil","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"George Peterzil","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 9190401, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 9190401, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058091437","display_name":"Johanna Steinmeyer","orcid":"https://orcid.org/0000-0002-0123-9545"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Johanna Steinmeyer","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 9190401, Jerusalem, Israel"],"raw_orcid":"https://orcid.org/0000-0002-0123-9545","affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, 9190401, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5093784772"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10271511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9965999722480774,"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/T11567","display_name":"semigroups and automata theory","score":0.9954000115394592,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9933000206947327,"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":0.7696664333343506},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6482299566268921},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6036683320999146},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5340370535850525},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36290639638900757},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13276901841163635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7696664333343506},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6482299566268921},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6036683320999146},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5340370535850525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36290639638900757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13276901841163635},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-02922-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02922-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02922-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-025-02922-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02922-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02922-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3929982605","display_name":null,"funder_award_id":"1832/19","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321950","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410144728.pdf","grobid_xml":"https://content.openalex.org/works/W4410144728.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1971361630","https://openalex.org/W2020913456","https://openalex.org/W2106177549","https://openalex.org/W2791853881","https://openalex.org/W3032777671","https://openalex.org/W4238284510","https://openalex.org/W4389300322"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"natural":[2],"numbers":[3],"$$k\\le":[4],"s\\le":[5],"n$$":[6],"<mml:math":[7,30],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[8,31],"<mml:mrow>":[9],"<mml:mi>k</mml:mi>":[10],"<mml:mo>\u2264</mml:mo>":[11,13],"<mml:mi>s</mml:mi>":[12],"<mml:mi>n</mml:mi>":[14],"</mml:mrow>":[15],"</mml:math>":[16,33],",":[17,63],"we":[18],"ask:":[19],"what":[20],"is":[21,60],"the":[22,73],"minimal":[23],"VC-dimension":[24],"of":[25,34,37,46,76],"a":[26,69],"family":[27],"$$\\mathcal":[28],"{F}$$":[29],"<mml:mi>F</mml:mi>":[32],"s":[35],"-subsets":[36,45],"[":[38,47],"n":[39,48,57],"]":[40],"that":[41,53],"covers":[42],"all":[43],"k":[44,62],"]?":[49],"We":[50],"first":[51],"show":[52],"for":[54,72],"sufficiently":[55],"large":[56],"this":[58,77],"number":[59],"always":[61],"and":[64],"construct":[65],"families":[66],"which":[67],"give":[68],"lower":[70],"bound":[71],"actual":[74],"growth":[75],"stabilization":[78],"point.":[79]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}