{"id":"https://openalex.org/W2151841298","doi":"https://doi.org/10.1017/s0963548301004977","title":"A Ratio Inequality for Binary Trees and the Best Secretary","display_name":"A Ratio Inequality for Binary Trees and the Best Secretary","publication_year":2002,"publication_date":"2002-03-01","ids":{"openalex":"https://openalex.org/W2151841298","doi":"https://doi.org/10.1017/s0963548301004977","mag":"2151841298"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548301004977","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548301004977","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/A5103031015","display_name":"Grzegorz Kubicki","orcid":"https://orcid.org/0000-0002-5531-167X"},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"GRZEGORZ KUBICKI","raw_affiliation_strings":["Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail:","Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail: gkubicki@louisville.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail:","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail: gkubicki@louisville.edu)#TAB#","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089439989","display_name":"Jen\u0151 Lehel","orcid":"https://orcid.org/0000-0003-4249-1082"},"institutions":[{"id":"https://openalex.org/I142740786","display_name":"University of Louisville","ror":"https://ror.org/01ckdn478","country_code":"US","type":"education","lineage":["https://openalex.org/I142740786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"JEN\u0150 LEHEL","raw_affiliation_strings":["Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail:","Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail: gkubicki@louisville.edu)#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail:","institution_ids":["https://openalex.org/I142740786"]},{"raw_affiliation_string":"Department of Mathematics, University of Louisville, Louisville, KY 40292, USA (e-mail: gkubicki@louisville.edu)#TAB#","institution_ids":["https://openalex.org/I142740786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033991835","display_name":"Micha\u0142 Morayne","orcid":"https://orcid.org/0000-0002-9856-479X"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"MICHA\u0141 MORAYNE","raw_affiliation_strings":["Institute of Mathematics, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50\u2013370 Wroc\u0142aw, Poland and Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51\u2013617 Wroc\u0142aw, Poland (e-mail:","Institute of Mathematics, Wroc\u0142aw Univ. of Tech., Wybrze\u017ce Wyspia\u0144skiego 27, 50\u2013370 Wroc\u0142aw and Inst. of Math., Polish Acad. Sci., Kopernika 18, 51\u2013617 Wroc\u0142aw "],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50\u2013370 Wroc\u0142aw, Poland and Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51\u2013617 Wroc\u0142aw, Poland (e-mail:","institution_ids":["https://openalex.org/I4210137370"]},{"raw_affiliation_string":"Institute of Mathematics, Wroc\u0142aw Univ. of Tech., Wybrze\u017ce Wyspia\u0144skiego 27, 50\u2013370 Wroc\u0142aw and Inst. of Math., Polish Acad. Sci., Kopernika 18, 51\u2013617 Wroc\u0142aw ","institution_ids":["https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":1.6787,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82654867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"2","first_page":"149","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994999766349792,"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":0.9994999766349792,"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/T12288","display_name":"Optimization and Search Problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/combinatorics","display_name":"Combinatorics","score":0.8634336590766907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7844830751419067},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7830314636230469},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6984039545059204},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5659238696098328},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5175737142562866},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5100293755531311},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.48679277300834656},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4441046714782715},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41347599029541016},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1345469057559967},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07104572653770447},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.06768950819969177}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8634336590766907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7844830751419067},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7830314636230469},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6984039545059204},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5659238696098328},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5175737142562866},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5100293755531311},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.48679277300834656},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4441046714782715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41347599029541016},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1345469057559967},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07104572653770447},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.06768950819969177},{"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:10.1017/s0963548301004977","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548301004977","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2019516620","https://openalex.org/W2051231039","https://openalex.org/W2057177502","https://openalex.org/W2068045918","https://openalex.org/W2116459287","https://openalex.org/W2576495983"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W4390961156","https://openalex.org/W1963087247","https://openalex.org/W4312224320","https://openalex.org/W2347443236","https://openalex.org/W4205203210","https://openalex.org/W2146274131","https://openalex.org/W2184328455","https://openalex.org/W2073211194","https://openalex.org/W2181347939"],"abstract_inverted_index":{"Let":[0],"Tn":[1,33,49],"be":[2],"the":[3,12,23,86,102,111],"complete":[4],"binary":[5,70],"tree":[6],"of":[7,15,101,110],"height":[8],"n":[9,67],"considered":[10],"as":[11,22],"Hasse":[13],"diagram":[14],"a":[16,78,107],"poset":[17,108],"with":[18,91],"its":[19],"root":[20],"1n":[21,35,51],"maximum":[24],"element.":[25],"Define":[26],"A(n;":[27],"T)":[28,44],"=":[29,45],"[mid":[30,46],"]{S":[31,47],"\u2286":[32,48],":":[34,50],"\u2208":[36],"S,":[37,53],"S":[38,54],"\u2245":[39,55],"T}[mid":[40,56],"],":[41],"and":[42,68],"B(n;":[43],"\u2209":[52],"].":[57],"In":[58],"this":[59],"note":[60],"we":[61],"prove":[62],"that":[63,75,85],"for":[64,93],"any":[65],"fixed":[66],"rooted":[69],"trees":[71],"T1,":[72],"T2":[73,76],"such":[74],"contains":[77],"subposet":[79],"isomorphic":[80],"to":[81],"T1.":[82],"We":[83],"conjecture":[84],"ratio":[87],"A/B":[88],"also":[89],"increases":[90],"T":[92],"arbitrary":[94],"trees.":[95],"These":[96],"inequalities":[97],"imply":[98],"natural":[99],"behaviour":[100],"optimal":[103],"stopping":[104],"time":[105],"in":[106],"extension":[109],"secretary":[112],"problem.":[113]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
