{"id":"https://openalex.org/W2549972378","doi":"https://doi.org/10.1007/s00493-017-3629-5","title":"The Probability of Generating the Symmetric Group","display_name":"The Probability of Generating the Symmetric Group","publication_year":2018,"publication_date":"2018-03-27","ids":{"openalex":"https://openalex.org/W2549972378","doi":"https://doi.org/10.1007/s00493-017-3629-5","mag":"2549972378"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-017-3629-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-017-3629-5","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.02501","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012226631","display_name":"Sean Eberhard","orcid":"https://orcid.org/0000-0003-3347-0976"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sean Eberhard","raw_affiliation_strings":["London, UK"],"affiliations":[{"raw_affiliation_string":"London, UK","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039145018","display_name":"Stefan-Christoph Virchow","orcid":null},"institutions":[{"id":"https://openalex.org/I4665924","display_name":"University of Rostock","ror":"https://ror.org/03zdwsf69","country_code":"DE","type":"education","lineage":["https://openalex.org/I4665924"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan-Christoph Virchow","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Rostock, Ulmenstr. 69 Haus 3, 18057, Rostock, Germany","Institut f\u00fcr Mathematik, Universit\u00e4t Rostock, Rostock, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Rostock, Ulmenstr. 69 Haus 3, 18057, Rostock, Germany","institution_ids":["https://openalex.org/I4665924"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Rostock, Rostock, Germany#TAB#","institution_ids":["https://openalex.org/I4665924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012226631"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04358812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"2","first_page":"273","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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/T10849","display_name":"Finite Group Theory Research","score":0.9983999729156494,"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":0.9908999800682068,"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/T11130","display_name":"Coding theory and cryptography","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.8176295161247253},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.8106139898300171},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.8043404817581177},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7665821313858032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7077360153198242},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6110159754753113},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5586879253387451},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.44969093799591064},{"id":"https://openalex.org/keywords/alternating-group","display_name":"Alternating group","score":0.43422722816467285},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34676700830459595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2159290313720703},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061899930238723755},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06078958511352539}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8176295161247253},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.8106139898300171},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.8043404817581177},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7665821313858032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7077360153198242},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6110159754753113},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5586879253387451},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.44969093799591064},{"id":"https://openalex.org/C38847919","wikidata":"https://www.wikidata.org/wiki/Q438814","display_name":"Alternating group","level":3,"score":0.43422722816467285},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34676700830459595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2159290313720703},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061899930238723755},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06078958511352539},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00493-017-3629-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-017-3629-5","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.02501","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.02501","pdf_url":"https://arxiv.org/pdf/1611.02501","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":"mag:2549972378","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1611.02501.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1611.02501","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1611.02501","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.02501","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.02501","pdf_url":"https://arxiv.org/pdf/1611.02501","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W120124575","https://openalex.org/W647209556","https://openalex.org/W1964902440","https://openalex.org/W1976372266","https://openalex.org/W2002472581","https://openalex.org/W2050269331","https://openalex.org/W2051170661","https://openalex.org/W2076973717","https://openalex.org/W2117519244","https://openalex.org/W2139572946","https://openalex.org/W2174141469","https://openalex.org/W2314376244","https://openalex.org/W2345533269","https://openalex.org/W2495029002","https://openalex.org/W2726936416","https://openalex.org/W2798943694","https://openalex.org/W3146127518","https://openalex.org/W4234295943"],"related_works":["https://openalex.org/W2963559975","https://openalex.org/W1658794775","https://openalex.org/W3003173879","https://openalex.org/W2007296129","https://openalex.org/W2900739425","https://openalex.org/W3114036815","https://openalex.org/W2950313797","https://openalex.org/W2406731817","https://openalex.org/W2807593659","https://openalex.org/W3034328592","https://openalex.org/W2092977611","https://openalex.org/W2963103801","https://openalex.org/W2052313090","https://openalex.org/W3100632772","https://openalex.org/W1536512642","https://openalex.org/W3147859549","https://openalex.org/W2135553523","https://openalex.org/W2336937548","https://openalex.org/W3194226021","https://openalex.org/W3012364704"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}