{"id":"https://openalex.org/W2126323192","doi":"https://doi.org/10.1017/s0963548312000247","title":"A Generalization of the Erd\u0151s\u2013Tur\u00e1n Law for the Order of Random Permutation","display_name":"A Generalization of the Erd\u0151s\u2013Tur\u00e1n Law for the Order of Random Permutation","publication_year":2012,"publication_date":"2012-07-03","ids":{"openalex":"https://openalex.org/W2126323192","doi":"https://doi.org/10.1017/s0963548312000247","mag":"2126323192"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548312000247","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000247","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074737766","display_name":"Alexander Gnedin","orcid":null},"institutions":[{"id":"https://openalex.org/I166337079","display_name":"Queen Mary University of London","ror":"https://ror.org/026zzn846","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I166337079"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"ALEXANDER GNEDIN","raw_affiliation_strings":["School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (e-mail:","School of mathematical sciences, queen mary, university of london, mile end road, london e1 4ns, uk (e-mail: a.gnedin@qmul.ac.uk)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (e-mail:","institution_ids":["https://openalex.org/I166337079"]},{"raw_affiliation_string":"School of mathematical sciences, queen mary, university of london, mile end road, london e1 4ns, uk (e-mail: a.gnedin@qmul.ac.uk)#TAB#","institution_ids":["https://openalex.org/I166337079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030507672","display_name":"Alexander Iksanov","orcid":"https://orcid.org/0000-0002-6764-7330"},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"ALEXANDER IKSANOV","raw_affiliation_strings":["Faculty of Cybernetics, Taras Shevchenko National University of Kiev, Kiev-01033, Ukraine (e-mail:","Faculty of cybernetics, taras shevchenko national university of kiev, kiev-01033, ukraine (e-mail: iksan@univ.kiev.ua, marynych@unicyb.kiev.ua)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Cybernetics, Taras Shevchenko National University of Kiev, Kiev-01033, Ukraine (e-mail:","institution_ids":["https://openalex.org/I189238007"]},{"raw_affiliation_string":"Faculty of cybernetics, taras shevchenko national university of kiev, kiev-01033, ukraine (e-mail: iksan@univ.kiev.ua, marynych@unicyb.kiev.ua)#TAB#","institution_ids":["https://openalex.org/I189238007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051774277","display_name":"Alexander Marynych","orcid":"https://orcid.org/0000-0002-7628-7541"},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"ALEXANDER MARYNYCH","raw_affiliation_strings":["Faculty of Cybernetics, Taras Shevchenko National University of Kiev, Kiev-01033, Ukraine (e-mail:","Faculty of cybernetics, taras shevchenko national university of kiev, kiev-01033, ukraine (e-mail: iksan@univ.kiev.ua, marynych@unicyb.kiev.ua)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Cybernetics, Taras Shevchenko National University of Kiev, Kiev-01033, Ukraine (e-mail:","institution_ids":["https://openalex.org/I189238007"]},{"raw_affiliation_string":"Faculty of cybernetics, taras shevchenko national university of kiev, kiev-01033, ukraine (e-mail: iksan@univ.kiev.ua, marynych@unicyb.kiev.ua)#TAB#","institution_ids":["https://openalex.org/I189238007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.13619787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"5","first_page":"715","last_page":"733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9825999736785889,"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/mathematics","display_name":"Mathematics","score":0.8262816667556763},{"id":"https://openalex.org/keywords/random-permutation","display_name":"Random permutation","score":0.7893295288085938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7458484172821045},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.732976496219635},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6536415815353394},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6189007759094238},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.5883094668388367},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5557509660720825},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5521581768989563},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5404546856880188},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5046528577804565},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.49277642369270325},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4428364932537079},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.24148032069206238},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13173234462738037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09330451488494873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07079291343688965}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8262816667556763},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.7893295288085938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7458484172821045},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.732976496219635},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6536415815353394},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6189007759094238},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.5883094668388367},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5557509660720825},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5521581768989563},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5404546856880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5046528577804565},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.49277642369270325},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4428364932537079},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.24148032069206238},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13173234462738037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09330451488494873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07079291343688965},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548312000247","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000247","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7599999904632568}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321010","display_name":"Universiteit Utrecht","ror":"https://ror.org/04pp8hn57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1235362104","https://openalex.org/W1479689787","https://openalex.org/W1484076335","https://openalex.org/W1489554514","https://openalex.org/W1495550473","https://openalex.org/W1529842847","https://openalex.org/W1551893515","https://openalex.org/W1564492869","https://openalex.org/W1596709027","https://openalex.org/W1631720620","https://openalex.org/W1984966799","https://openalex.org/W1990871665","https://openalex.org/W2001879439","https://openalex.org/W2003535049","https://openalex.org/W2005085536","https://openalex.org/W2031769296","https://openalex.org/W2053390290","https://openalex.org/W2054940035","https://openalex.org/W2068312480","https://openalex.org/W2099412267","https://openalex.org/W2103268360","https://openalex.org/W2105183600","https://openalex.org/W2109191002","https://openalex.org/W2132297389","https://openalex.org/W2137601763","https://openalex.org/W2165782593","https://openalex.org/W2313299119","https://openalex.org/W2595665432","https://openalex.org/W2950429760","https://openalex.org/W3099189739","https://openalex.org/W3100298211","https://openalex.org/W4230925302","https://openalex.org/W4237823923","https://openalex.org/W4300223101","https://openalex.org/W6628965497"],"related_works":["https://openalex.org/W2184131469","https://openalex.org/W4321748008","https://openalex.org/W2797610470","https://openalex.org/W2074196947","https://openalex.org/W1887300513","https://openalex.org/W4312051210","https://openalex.org/W4297729179","https://openalex.org/W2120153268","https://openalex.org/W2533058927","https://openalex.org/W102744014"],"abstract_inverted_index":{"We":[0],"consider":[1],"random":[2,86],"permutations":[3,66,72],"derived":[4],"by":[5],"sampling":[6,75],"from":[7,76],"stick-breaking":[8,40],"partitions":[9],"of":[10,17,27,51,54,96,98],"the":[11,25,39,49,52,55,59,64,77,90,94,99],"unit":[12],"interval.":[13],"The":[14],"cycle":[15,100],"structure":[16],"such":[18],"a":[19,28,44],"permutation":[20],"can":[21],"be":[22],"associated":[23,73],"with":[24,74],"path":[26],"decreasing":[29],"Markov":[30],"chain":[31],"on":[32,38,83],"n":[33],"integers.":[34],"Under":[35],"certain":[36],"assumptions":[37],"factor":[41],"we":[42],"prove":[43],"central":[45],"limit":[46,91],"theorem":[47],"for":[48,63,70,93],"logarithm":[50],"order":[53],"permutation,":[56],"thus":[57],"extending":[58],"classical":[60],"Erd\u0151s\u2013Tur\u00e1n":[61],"law":[62],"uniform":[65],"and":[67],"its":[68],"generalization":[69],"Ewens'":[71],"PD/GEM(\u03b8)-distribution.":[78],"Our":[79],"approach":[80],"is":[81],"based":[82],"using":[84],"perturbed":[85],"walks":[87],"to":[88],"obtain":[89],"laws":[92],"sum":[95],"logarithms":[97],"lengths.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
