{"id":"https://openalex.org/W2118739731","doi":"https://doi.org/10.37236/1714","title":"Two-Stage Allocations and the Double $Q$-Function","display_name":"Two-Stage Allocations and the Double $Q$-Function","publication_year":2003,"publication_date":"2003-05-12","ids":{"openalex":"https://openalex.org/W2118739731","doi":"https://doi.org/10.37236/1714","mag":"2118739731"},"language":"en","primary_location":{"id":"doi:10.37236/1714","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1714","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r21/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/v10i1r21/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000528383","display_name":"Sergey Agievich","orcid":"https://orcid.org/0000-0002-9413-8574"},"institutions":[{"id":"https://openalex.org/I291386647","display_name":"Belarusian State University","ror":"https://ror.org/021036w13","country_code":"BY","type":"education","lineage":["https://openalex.org/I291386647"]}],"countries":["BY"],"is_corresponding":true,"raw_author_name":"Sergey Agievich","raw_affiliation_strings":["Belarusian State University Fr. Skorina av. 4, 220050 Minsk, Belarus","National Research Center for Applied Problems of Mathematics and Informatics"],"affiliations":[{"raw_affiliation_string":"Belarusian State University Fr. Skorina av. 4, 220050 Minsk, Belarus","institution_ids":["https://openalex.org/I291386647"]},{"raw_affiliation_string":"National Research Center for Applied Problems of Mathematics and Informatics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000528383"],"corresponding_institution_ids":["https://openalex.org/I291386647"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.20994475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","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":0.9998999834060669,"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":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"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/combinatorics","display_name":"Combinatorics","score":0.7014439105987549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6940881013870239},{"id":"https://openalex.org/keywords/falling","display_name":"Falling (accident)","score":0.6703583598136902},{"id":"https://openalex.org/keywords/stage","display_name":"Stage (stratigraphy)","score":0.5127812027931213},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.5006167888641357},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44685015082359314},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4261765480041504},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3316913843154907}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7014439105987549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6940881013870239},{"id":"https://openalex.org/C2779079380","wikidata":"https://www.wikidata.org/wiki/Q333495","display_name":"Falling (accident)","level":2,"score":0.6703583598136902},{"id":"https://openalex.org/C146357865","wikidata":"https://www.wikidata.org/wiki/Q1123245","display_name":"Stage (stratigraphy)","level":2,"score":0.5127812027931213},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.5006167888641357},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44685015082359314},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4261765480041504},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3316913843154907},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C99454951","wikidata":"https://www.wikidata.org/wiki/Q932068","display_name":"Environmental health","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1714","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1714","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r21/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.1299","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.1299","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/Volume_10/PDF/v10i1r21.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.7826","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.7826","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/Volume_10/PostScriptfiles/v10i1r21.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1714","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1714","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v10i1r21/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/W2118739731.pdf","grobid_xml":"https://content.openalex.org/works/W2118739731.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W82672431","https://openalex.org/W606453859","https://openalex.org/W1971352841","https://openalex.org/W2018919817","https://openalex.org/W2030644481","https://openalex.org/W2044702122","https://openalex.org/W2059140607","https://openalex.org/W2167266655","https://openalex.org/W2324608937","https://openalex.org/W2751862591","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W4301441647"],"related_works":["https://openalex.org/W2024194626","https://openalex.org/W4386475327","https://openalex.org/W2386158341","https://openalex.org/W2746852369","https://openalex.org/W1976940922","https://openalex.org/W2374649224","https://openalex.org/W2332777286","https://openalex.org/W2389533097","https://openalex.org/W2357343611","https://openalex.org/W2039981404"],"abstract_inverted_index":{"Let":[0,39],"$m+n$":[1],"particles":[2,21,45,63],"be":[3,83],"thrown":[4],"randomly,":[5],"independently":[6],"of":[7,29,72,86],"each":[8],"other":[9,61],"into":[10,33,76,92],"$N$":[11],"cells,":[12],"using":[13],"the":[14,27,40,53,58,70,77,84,87,97,107],"following":[15],"two-stage":[16],"procedure.1.":[17],"The":[18,60],"first":[19,88],"$m$":[20],"are":[22,64],"allocated":[23,66],"equiprobably,":[24],"that":[25,68,90],"is,":[26,69],"probability":[28,54,71],"a":[30,73,93],"particle":[31,74,89],"falling":[32,75],"any":[34],"particular":[35],"cell":[36,42,52,79,95],"is":[37,80],"$1/N$.":[38],"$i$th":[41,78],"contain":[43],"$m_i$":[44],"on":[46],"completion.":[47],"Then":[48],"associate":[49],"with":[50],"this":[51],"$a_i=m_i/m$":[55],"and":[56,103],"withdraw":[57],"particles.2.":[59],"$n$":[62],"then":[65],"polynomially,":[67],"$a_i$.Let":[81],"$\\nu=\\nu(m,N)$":[82],"number":[85],"falls":[91],"non-empty":[94],"during":[96],"second":[98],"stage.":[99],"We":[100],"give":[101],"exact":[102],"asymptotic":[104],"expressions":[105],"for":[106],"expectation":[108],"${\\bf":[109],"E}\\nu$.":[110]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}