{"id":"https://openalex.org/W1583696788","doi":"https://doi.org/10.37236/5112","title":"The Parametric Frobenius Problem","display_name":"The Parametric Frobenius Problem","publication_year":2015,"publication_date":"2015-05-22","ids":{"openalex":"https://openalex.org/W1583696788","doi":"https://doi.org/10.37236/5112","mag":"1583696788"},"language":"en","primary_location":{"id":"doi:10.37236/5112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p36/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p36/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032243537","display_name":"Bjarke Hammersholt Roune","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bjarke Hammersholt Roune","raw_affiliation_strings":["University of Kaiserslautern","University of Kaiserslautern;"],"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"University of Kaiserslautern;","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008278795","display_name":"Kevin M. Woods","orcid":"https://orcid.org/0000-0002-0198-6129"},"institutions":[{"id":"https://openalex.org/I70571728","display_name":"Oberlin College","ror":"https://ror.org/05ac26z88","country_code":"US","type":"education","lineage":["https://openalex.org/I70571728"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin Woods","raw_affiliation_strings":["Oberlin College","Oberlin College >  >  >  >"],"affiliations":[{"raw_affiliation_string":"Oberlin College","institution_ids":["https://openalex.org/I70571728"]},{"raw_affiliation_string":"Oberlin College >  >  >  >","institution_ids":["https://openalex.org/I70571728"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032243537"],"corresponding_institution_ids":["https://openalex.org/I153267046"],"apc_list":null,"apc_paid":null,"fwci":0.31430091,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78416844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9993000030517578,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9988999962806702,"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/mathematics","display_name":"Mathematics","score":0.7991043329238892},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.712563157081604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6906746029853821},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6471133828163147},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5968114137649536},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5224008560180664},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46582740545272827},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.4639629125595093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.459757536649704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7991043329238892},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.712563157081604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6906746029853821},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6471133828163147},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5968114137649536},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5224008560180664},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46582740545272827},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.4639629125595093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.459757536649704},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/5112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p36/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1502.06009","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.06009","pdf_url":"https://arxiv.org/pdf/1502.06009","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1583696788","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1502.06009","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.702.115","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.702.115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.oberlin.edu/faculty/kwoods/research/parfrob.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1502.06009","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1502.06009","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/5112","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5112","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p36/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/W1583696788.pdf","grobid_xml":"https://content.openalex.org/works/W1583696788.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W229079384","https://openalex.org/W2000197435","https://openalex.org/W2072219837","https://openalex.org/W2116603945","https://openalex.org/W2595839407","https://openalex.org/W2952672952","https://openalex.org/W2964003753"],"related_works":["https://openalex.org/W2206022628","https://openalex.org/W1594880732","https://openalex.org/W2048106386","https://openalex.org/W2951973587","https://openalex.org/W3046993266","https://openalex.org/W3101150706","https://openalex.org/W2964149052","https://openalex.org/W2953162326","https://openalex.org/W2973063050","https://openalex.org/W2128040351","https://openalex.org/W2899984794","https://openalex.org/W3129032914","https://openalex.org/W2077117201","https://openalex.org/W2405068759","https://openalex.org/W2984220964","https://openalex.org/W2016620090","https://openalex.org/W2217597875","https://openalex.org/W2588436294","https://openalex.org/W2963968913"],"abstract_inverted_index":{"Given":[0],"relatively":[1],"prime":[2],"positive":[3],"integers":[4],"$a_1,\\ldots,a_n$,":[5],"the":[6,10,23,27,40,74,83,98,101,111],"Frobenius":[7,41,84],"number":[8,42,85,116],"is":[9,51,119],"largest":[11],"integer":[12,20],"that":[13,64],"cannot":[14],"be":[15],"written":[16],"as":[17,35,43],"a":[18,44,52,57,88],"nonnegative":[19],"combination":[21],"of":[22,30,37,46,117],"$a_i$.":[24],"We":[25,70,94],"examine":[26],"parametric":[28],"version":[29],"this":[31,96],"problem:":[32],"given":[33],"$a_i=a_i(t)$":[34],"functions":[36],"$t$,":[38,81],"compute":[39],"function":[45,49],"$t$.":[47,69,93],"A":[48],"$f:\\mathbb{Z}_+\\rightarrow\\mathbb{Z}$":[50],"quasi-polynomial":[53],"if":[54,73],"there":[55],"exists":[56],"period":[58],"$m$":[59],"and":[60,106],"polynomials":[61,77],"$f_0,\\ldots,f_{m-1}$":[62],"such":[63],"$f(t)=f_{t\\bmod":[65],"m}(t)$":[66],"for":[67,90],"all":[68],"conjecture":[71],"that,":[72],"$a_i(t)$":[75,102],"are":[76,103],"(or":[78],"quasi-polynomials)":[79],"in":[80,97,110],"then":[82],"agrees":[86],"with":[87],"quasi-polynomial,":[89],"sufficiently":[91],"large":[92],"prove":[95,108],"case":[99,112],"where":[100,113],"linear":[104],"functions,":[105],"also":[107],"it":[109],"$n$":[114],"(the":[115],"generators)":[118],"at":[120],"most":[121],"3.":[122]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
