{"id":"https://openalex.org/W2103597166","doi":"https://doi.org/10.37236/1307","title":"Asymptotics of Young Diagrams and Hook Numbers","display_name":"Asymptotics of Young Diagrams and Hook Numbers","publication_year":1997,"publication_date":"1997-09-21","ids":{"openalex":"https://openalex.org/W2103597166","doi":"https://doi.org/10.37236/1307","mag":"2103597166"},"language":"en","primary_location":{"id":"doi:10.37236/1307","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1307","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072787171","display_name":"Amitai Regev","orcid":"https://orcid.org/0000-0002-3625-7655"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]},{"id":"https://openalex.org/I4210102560","display_name":"Israel Institute for Advanced Studies","ror":"https://ror.org/01140r423","country_code":"IL","type":"facility","lineage":["https://openalex.org/I4210102560"]},{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Amitai Regev","raw_affiliation_strings":["The Institute for Advanced Studies of the Hebrew University Givat Ram Jerusalem, Israel","Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A","Department of Theoretical Mathematics The Weizmann Institute of Science Rehovot 76100, Israel","St. Petersburg branch of the Mathematics Institute of the Russian Academy of Science Fontanka 27 St. Petersburg, 191011 Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute for Advanced Studies of the Hebrew University Givat Ram Jerusalem, Israel","institution_ids":["https://openalex.org/I4210102560"]},{"raw_affiliation_string":"Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Theoretical Mathematics The Weizmann Institute of Science Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"St. Petersburg branch of the Mathematics Institute of the Russian Academy of Science Fontanka 27 St. Petersburg, 191011 Russia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111417644","display_name":"A. M. Vershik","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]},{"id":"https://openalex.org/I4210102560","display_name":"Israel Institute for Advanced Studies","ror":"https://ror.org/01140r423","country_code":"IL","type":"facility","lineage":["https://openalex.org/I4210102560"]},{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Anatoly Vershik","raw_affiliation_strings":["St. Petersburg branch of the Mathematics Institute of the Russian Academy of Science Fontanka 27 St. Petersburg, 191011 Russia","Department of Theoretical Mathematics The Weizmann Institute of Science Rehovot 76100, Israel","The Institute for Advanced Studies of the Hebrew University Givat Ram Jerusalem, Israel","Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"St. Petersburg branch of the Mathematics Institute of the Russian Academy of Science Fontanka 27 St. Petersburg, 191011 Russia","institution_ids":[]},{"raw_affiliation_string":"Department of Theoretical Mathematics The Weizmann Institute of Science Rehovot 76100, Israel","institution_ids":["https://openalex.org/I53964585"]},{"raw_affiliation_string":"The Institute for Advanced Studies of the Hebrew University Givat Ram Jerusalem, Israel","institution_ids":["https://openalex.org/I4210102560"]},{"raw_affiliation_string":"Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5554,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95776892,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","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":1.0,"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":1.0,"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":0.9983999729156494,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8171749114990234},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.812624454498291},{"id":"https://openalex.org/keywords/hook","display_name":"Hook","score":0.8056707382202148},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.7710161209106445},{"id":"https://openalex.org/keywords/young-tableau","display_name":"Young tableau","score":0.7418749332427979},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6518441438674927},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5997958183288574},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5815662741661072},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.5631649494171143},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.5357977747917175},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4638827443122864},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3409603536128998},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07804325222969055},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05524706840515137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8171749114990234},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.812624454498291},{"id":"https://openalex.org/C2777586403","wikidata":"https://www.wikidata.org/wiki/Q4243098","display_name":"Hook","level":2,"score":0.8056707382202148},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.7710161209106445},{"id":"https://openalex.org/C165368118","wikidata":"https://www.wikidata.org/wiki/Q2166280","display_name":"Young tableau","level":2,"score":0.7418749332427979},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6518441438674927},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5997958183288574},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5815662741661072},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.5631649494171143},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.5357977747917175},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4638827443122864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3409603536128998},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07804325222969055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05524706840515137},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1307","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1307","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/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":false,"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"}],"best_oa_location":{"id":"doi:10.37236/1307","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1307","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v4i1r22/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":false,"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2103597166.pdf","grobid_xml":"https://content.openalex.org/works/W2103597166.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1679486839","https://openalex.org/W2044716712","https://openalex.org/W2134984950"],"related_works":["https://openalex.org/W3170859598","https://openalex.org/W1987461188","https://openalex.org/W2949146761","https://openalex.org/W3193656016","https://openalex.org/W4297742872","https://openalex.org/W1667518552","https://openalex.org/W2970082198","https://openalex.org/W2901313923","https://openalex.org/W2994188339","https://openalex.org/W4225633054"],"abstract_inverted_index":{"Asymptotic":[0],"calculations":[1],"are":[2,28,86],"applied":[3],"to":[4,30,95],"study":[5,73],"the":[6,39,72,75,106,114,117],"degrees":[7],"of":[8,11,13,41,65,74,81,90,101,109,113,116],"certain":[9],"sequences":[10],"characters":[12],"symmetric":[14,118],"groups.":[15,119],"Starting":[16],"with":[17],"a":[18],"given":[19],"partition":[20],"$\\mu$,":[21],"we":[22,48],"deduce":[23],"several":[24],"skew":[25,35],"diagrams":[26],"which":[27],"related":[29],"$\\mu$.":[31],"To":[32],"each":[33],"such":[34],"diagram":[36],"there":[37],"corresponds":[38],"product":[40],"its":[42],"hook":[43,76],"numbers.":[44],"By":[45],"asymptotic":[46,107],"methods":[47],"obtain":[49],"some":[50],"unexpected":[51],"arithmetic":[52],"properties":[53,89],"between":[54],"these":[55,66,102],"products.":[56],"The":[57,68,84,99],"authors":[58],"do":[59],"not":[60],"know":[61],"\"finite\",":[62],"nonasymptotic":[63],"proofs":[64,85],"results.":[67],"problem":[69],"appeared":[70],"in":[71],"formula":[77],"for":[78],"various":[79],"kinds":[80],"Young":[82],"diagrams.":[83],"based":[87],"on":[88],"shifted":[91],"Schur":[92],"functions,":[93],"due":[94],"Okounkov":[96],"and":[97,111],"Olshanski.":[98],"theory":[100,108],"functions":[103],"arose":[104],"from":[105],"Vershik":[110],"Kerov":[112],"representations":[115]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}