{"id":"https://openalex.org/W2149474543","doi":"https://doi.org/10.37236/723","title":"Convergence Rates for Generalized Descents","display_name":"Convergence Rates for Generalized Descents","publication_year":2011,"publication_date":"2011-12-19","ids":{"openalex":"https://openalex.org/W2149474543","doi":"https://doi.org/10.37236/723","mag":"2149474543"},"language":"en","primary_location":{"id":"doi:10.37236/723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p236/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":true,"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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p236/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045667403","display_name":"John Pike","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I2800817003","display_name":"California Southern University","ror":"https://ror.org/058zz0t50","country_code":"US","type":"education","lineage":["https://openalex.org/I2800817003"]},{"id":"https://openalex.org/I903300897","display_name":"Southern States University","ror":"https://ror.org/01b0j0m34","country_code":"US","type":"education","lineage":["https://openalex.org/I903300897"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John Pike","raw_affiliation_strings":["Department of Mathematics University of Southern California, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Southern California, U.S.A","institution_ids":["https://openalex.org/I903300897","https://openalex.org/I1174212","https://openalex.org/I2800817003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045667403"],"corresponding_institution_ids":["https://openalex.org/I1174212","https://openalex.org/I2800817003","https://openalex.org/I903300897"],"apc_list":null,"apc_paid":null,"fwci":0.4476,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.6235184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"1","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":0.9995999932289124,"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":0.9995999932289124,"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/T11716","display_name":"Random Matrices and Applications","score":0.9994000196456909,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9973999857902527,"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/mathematics","display_name":"Mathematics","score":0.8888142108917236},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6669646501541138},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6398566961288452},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.6337578296661377},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.5688485503196716},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5593125820159912},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5192790031433105},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.502025842666626},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4765266180038452},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4519491195678711},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3968965411186218},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28854894638061523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08079785108566284},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06914275884628296}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8888142108917236},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6669646501541138},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6398566961288452},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6337578296661377},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.5688485503196716},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5593125820159912},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5192790031433105},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.502025842666626},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4765266180038452},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4519491195678711},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3968965411186218},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28854894638061523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08079785108566284},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06914275884628296},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p236/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":true,"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:10.1.1.372.8673","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.8673","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/ojs/index.php/eljc/article/viewFile/v18i1p236/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/723","is_oa":true,"landing_page_url":"https://doi.org/10.37236/723","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p236/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":true,"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":[{"display_name":"Reduced inequalities","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2149474543.pdf","grobid_xml":"https://content.openalex.org/works/W2149474543.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1587704401","https://openalex.org/W1596709027","https://openalex.org/W1600293573","https://openalex.org/W1606092140","https://openalex.org/W1976069242","https://openalex.org/W2059899875","https://openalex.org/W2169071224","https://openalex.org/W2171776255","https://openalex.org/W2290340109","https://openalex.org/W2576544140","https://openalex.org/W2999453069"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W4229993731","https://openalex.org/W2381059884","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2220405813","https://openalex.org/W3123626006","https://openalex.org/W3123025204","https://openalex.org/W1988122674"],"abstract_inverted_index":{"d-descents":[0,19],"are":[1],"permutation":[2],"statistics":[3,47],"that":[4,15],"generalize":[5],"the":[6,16,41,52],"notions":[7],"of":[8,18,20,22,45,54],"descents":[9],"and":[10,43,48],"inversions.":[11],"It":[12],"is":[13],"known":[14],"distribution":[17],"permutations":[21],"length":[23],"n":[24,31],"satisfies":[25],"a":[26],"central":[27],"limit":[28],"theorem":[29],"as":[30],"goes":[32],"to":[33],"infinity.":[34],"We":[35],"provide":[36],"an":[37],"explicit":[38],"formula":[39],"for":[40],"mean":[42],"variance":[44],"these":[46],"obtain":[49],"bounds":[50],"on":[51],"rate":[53],"convergence":[55],"using":[56],"Stein's":[57],"method.":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}