{"id":"https://openalex.org/W1854868231","doi":"https://doi.org/10.1007/3-540-45446-2_21","title":"Coupon Collectors, q-Binomial Coefficients and the Unsatisfiability Threshold","display_name":"Coupon Collectors, q-Binomial Coefficients and the Unsatisfiability Threshold","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1854868231","doi":"https://doi.org/10.1007/3-540-45446-2_21","mag":"1854868231"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-45446-2_21","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45446-2_21","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5030699433","display_name":"Alexis C. Kaporis","orcid":null},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Alexis C. Kaporis","raw_affiliation_strings":["Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","University of Patras;"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"University of Patras;","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024610751","display_name":"Lefteris M. Kirousis","orcid":"https://orcid.org/0000-0002-4912-8959"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Lefteris M. Kirousis","raw_affiliation_strings":["Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","University of Patras;"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"University of Patras;","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025854118","display_name":"Yannis C. Stamatiou","orcid":"https://orcid.org/0000-0002-8925-9427"},"institutions":[{"id":"https://openalex.org/I120729142","display_name":"Research Academic Computer Technology Institute","ror":"https://ror.org/021nszj63","country_code":"GR","type":"facility","lineage":["https://openalex.org/I120729142","https://openalex.org/I4210154149"]},{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Yannis C. Stamatiou","raw_affiliation_strings":["Computer Technology Institute, Kolokotroni 3, 26321, Patras, Greece","Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","Computer Technology Institute","Univ. of Patras"],"affiliations":[{"raw_affiliation_string":"Computer Technology Institute, Kolokotroni 3, 26321, Patras, Greece","institution_ids":["https://openalex.org/I120729142"]},{"raw_affiliation_string":"Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"Computer Technology Institute","institution_ids":["https://openalex.org/I120729142"]},{"raw_affiliation_string":"Univ. of Patras","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013929795","display_name":"Malvina Vamvakari","orcid":"https://orcid.org/0000-0002-3381-3257"},"institutions":[{"id":"https://openalex.org/I174878644","display_name":"University of Patras","ror":"https://ror.org/017wvtq80","country_code":"GR","type":"education","lineage":["https://openalex.org/I174878644"]},{"id":"https://openalex.org/I120729142","display_name":"Research Academic Computer Technology Institute","ror":"https://ror.org/021nszj63","country_code":"GR","type":"facility","lineage":["https://openalex.org/I120729142","https://openalex.org/I4210154149"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Malvina Vamvakari","raw_affiliation_strings":["Computer Technology Institute, Kolokotroni 3, 26321, Patras, Greece","Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","Computer Technology Institute","Univ. of Patras"],"affiliations":[{"raw_affiliation_string":"Computer Technology Institute, Kolokotroni 3, 26321, Patras, Greece","institution_ids":["https://openalex.org/I120729142"]},{"raw_affiliation_string":"Department of Computer Engineering and Informatics, University of Patras, Rio 265 00, Patras, Greece","institution_ids":["https://openalex.org/I174878644"]},{"raw_affiliation_string":"Computer Technology Institute","institution_ids":["https://openalex.org/I120729142"]},{"raw_affiliation_string":"Univ. of Patras","institution_ids":["https://openalex.org/I174878644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013505086","display_name":"Michele Zito","orcid":null},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michele Zito","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, UK","#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5030699433"],"corresponding_institution_ids":["https://openalex.org/I174878644"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0313,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.79707113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"328","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9962999820709229,"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"}},"topics":[{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9962999820709229,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9585000276565552,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9398999810218811,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7924193739891052},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.6584725975990295},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6433224678039551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.599073588848114},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5595617294311523},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5102963447570801},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5024256706237793},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.4868904650211334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4622046947479248},{"id":"https://openalex.org/keywords/binomial-theorem","display_name":"Binomial theorem","score":0.4614063799381256},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45535778999328613},{"id":"https://openalex.org/keywords/binomial-distribution","display_name":"Binomial distribution","score":0.4130176901817322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24831196665763855},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2236264944076538},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12439677119255066}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7924193739891052},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.6584725975990295},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6433224678039551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.599073588848114},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5595617294311523},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5102963447570801},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5024256706237793},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.4868904650211334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4622046947479248},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.4614063799381256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45535778999328613},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.4130176901817322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24831196665763855},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2236264944076538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12439677119255066},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-45446-2_21","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-45446-2_21","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.28.8766","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.28.8766","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.liv.ac.uk/~michele/PAPERI/ictcs.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W73235108","https://openalex.org/W82672431","https://openalex.org/W242035403","https://openalex.org/W1489988510","https://openalex.org/W1523650025","https://openalex.org/W1559492868","https://openalex.org/W1999803716","https://openalex.org/W2000931246","https://openalex.org/W2008052995","https://openalex.org/W2068728923","https://openalex.org/W2068871408","https://openalex.org/W2077154649","https://openalex.org/W2130956934","https://openalex.org/W2131459042","https://openalex.org/W2132240307","https://openalex.org/W2196559987","https://openalex.org/W2295428206","https://openalex.org/W2575871956","https://openalex.org/W2905110430","https://openalex.org/W4212799367","https://openalex.org/W4231916799","https://openalex.org/W4301168112","https://openalex.org/W6603367127","https://openalex.org/W6633749307","https://openalex.org/W6667812997"],"related_works":["https://openalex.org/W3081861082","https://openalex.org/W4320152868","https://openalex.org/W3121198759","https://openalex.org/W2780957143","https://openalex.org/W2955220190","https://openalex.org/W2047523883","https://openalex.org/W1619654942","https://openalex.org/W4295127428","https://openalex.org/W2788993398","https://openalex.org/W4281893131"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
