{"id":"https://openalex.org/W1488679966","doi":"https://doi.org/10.1007/978-3-540-85780-8_5","title":"The Frobenius Problem and Its Generalizations","display_name":"The Frobenius Problem and Its Generalizations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1488679966","doi":"https://doi.org/10.1007/978-3-540-85780-8_5","mag":"1488679966"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-85780-8_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85780-8_5","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/A5065322269","display_name":"Jeffrey Shallit","orcid":"https://orcid.org/0000-0003-1197-3820"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jeffrey Shallit","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","School of Computer Science, University of Waterloo, Waterloo, Canada, ON, N2L 3G1#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, Canada, ON, N2L 3G1#TAB#","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065322269"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":2.7458,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.91584158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"72","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9977999925613403,"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/T11130","display_name":"Coding theory and cryptography","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.8923221826553345},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.679347813129425},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5376502275466919},{"id":"https://openalex.org/keywords/radical-of-an-integer","display_name":"Radical of an integer","score":0.4702186584472656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4379645884037018},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15905490517616272},{"id":"https://openalex.org/keywords/prime-factor","display_name":"Prime factor","score":0.10533884167671204}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8923221826553345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.679347813129425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5376502275466919},{"id":"https://openalex.org/C203432157","wikidata":"https://www.wikidata.org/wiki/Q2498974","display_name":"Radical of an integer","level":4,"score":0.4702186584472656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4379645884037018},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15905490517616272},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.10533884167671204},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.0},{"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:10.1007/978-3-540-85780-8_5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-85780-8_5","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1689345","https://openalex.org/W811340882","https://openalex.org/W1504647293","https://openalex.org/W1506489923","https://openalex.org/W1529791103","https://openalex.org/W1539025858","https://openalex.org/W1557880231","https://openalex.org/W1969549783","https://openalex.org/W1971747251","https://openalex.org/W1972272347","https://openalex.org/W2000197435","https://openalex.org/W2003926749","https://openalex.org/W2006629323","https://openalex.org/W2012188345","https://openalex.org/W2035580504","https://openalex.org/W2048325117","https://openalex.org/W2048489261","https://openalex.org/W2062513475","https://openalex.org/W2075025003","https://openalex.org/W2092017668","https://openalex.org/W2104550739","https://openalex.org/W2116603945","https://openalex.org/W2119539951","https://openalex.org/W2128548465","https://openalex.org/W2316176421","https://openalex.org/W2319549236","https://openalex.org/W2332901121","https://openalex.org/W2335606727","https://openalex.org/W4234554463","https://openalex.org/W4245656449","https://openalex.org/W4247452726","https://openalex.org/W6604285789"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1253992879","https://openalex.org/W2377903368","https://openalex.org/W2133840515","https://openalex.org/W766797309","https://openalex.org/W2185598862","https://openalex.org/W2552939527","https://openalex.org/W3082806270","https://openalex.org/W2155895766","https://openalex.org/W2332490159"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}