{"id":"https://openalex.org/W2932051495","doi":"https://doi.org/10.1080/00029890.2020.1674073","title":"Increasingly Enumerable Submonoids of R: Music Theory as a Unifying Theme","display_name":"Increasingly Enumerable Submonoids of R: Music Theory as a Unifying Theme","publication_year":2019,"publication_date":"2019-12-19","ids":{"openalex":"https://openalex.org/W2932051495","doi":"https://doi.org/10.1080/00029890.2020.1674073","mag":"2932051495"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1674073","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1674073","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/1904.02897.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021954232","display_name":"Maria Bras-Amor\u00f3s","orcid":"https://orcid.org/0000-0002-3481-004X"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Maria Bras-Amor\u00f3s","raw_affiliation_strings":["Department of Computer Science and Mathematics, Universitat Rovira i Virgili","Department of Computer Science and Mathematics, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, Tarragona 43007, Catalonia, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Mathematics, Universitat Rovira i Virgili","institution_ids":["https://openalex.org/I55952717"]},{"raw_affiliation_string":"Department of Computer Science and Mathematics, Universitat Rovira i Virgili, Av. Pa\u00efsos Catalans 26, Tarragona 43007, Catalonia, Spain","institution_ids":["https://openalex.org/I55952717"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021954232"],"corresponding_institution_ids":["https://openalex.org/I55952717"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11051719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"127","issue":"1","first_page":"33","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9908999800682068,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9908999800682068,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.982699990272522,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9796000123023987,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/monoid","display_name":"Monoid","score":0.8307509422302246},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.6645928025245667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6638530492782593},{"id":"https://openalex.org/keywords/commensurability","display_name":"Commensurability (mathematics)","score":0.6330817937850952},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.5731157064437866},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5199831128120422},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5063382387161255},{"id":"https://openalex.org/keywords/recursively-enumerable-set","display_name":"Recursively enumerable set","score":0.4856904447078705},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43685993552207947},{"id":"https://openalex.org/keywords/maximal-set","display_name":"Maximal set","score":0.430636465549469},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.40538161993026733},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39399486780166626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34280312061309814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15766412019729614},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1168442964553833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09369206428527832}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.8307509422302246},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.6645928025245667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6638530492782593},{"id":"https://openalex.org/C119350121","wikidata":"https://www.wikidata.org/wiki/Q1091134","display_name":"Commensurability (mathematics)","level":2,"score":0.6330817937850952},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5731157064437866},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5199831128120422},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5063382387161255},{"id":"https://openalex.org/C52703633","wikidata":"https://www.wikidata.org/wiki/Q676835","display_name":"Recursively enumerable set","level":3,"score":0.4856904447078705},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43685993552207947},{"id":"https://openalex.org/C188521023","wikidata":"https://www.wikidata.org/wiki/Q6795644","display_name":"Maximal set","level":3,"score":0.430636465549469},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.40538161993026733},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39399486780166626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34280312061309814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15766412019729614},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1168442964553833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09369206428527832},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00029890.2020.1674073","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1674073","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"mag:2932051495","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1904.02897.pdf","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":"doi:10.48550/arxiv.1904.02897","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.02897","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"}],"best_oa_location":{"id":"mag:2932051495","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1904.02897.pdf","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},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1975129488","https://openalex.org/W1988000615","https://openalex.org/W1998537439","https://openalex.org/W1999043701","https://openalex.org/W2004577463","https://openalex.org/W2060844765","https://openalex.org/W2109158132","https://openalex.org/W2139797601","https://openalex.org/W2157726910","https://openalex.org/W2165060009","https://openalex.org/W2469506186","https://openalex.org/W2516738267","https://openalex.org/W2544600950","https://openalex.org/W2927879600","https://openalex.org/W2952470349","https://openalex.org/W2963655230","https://openalex.org/W3099349302","https://openalex.org/W3102181942","https://openalex.org/W3104795092","https://openalex.org/W4236438420","https://openalex.org/W4252810166","https://openalex.org/W4390009472"],"related_works":["https://openalex.org/W2624688418","https://openalex.org/W2083427293","https://openalex.org/W2075791193","https://openalex.org/W2953051185","https://openalex.org/W2611135773","https://openalex.org/W1626979325","https://openalex.org/W1999298839","https://openalex.org/W2777477031","https://openalex.org/W3102200253","https://openalex.org/W3009496221","https://openalex.org/W2586008757","https://openalex.org/W1489736929","https://openalex.org/W2656886257","https://openalex.org/W757345910","https://openalex.org/W82679384","https://openalex.org/W3099339315","https://openalex.org/W1972641171","https://openalex.org/W2524361808","https://openalex.org/W2116250539","https://openalex.org/W3002791456"],"abstract_inverted_index":{"We":[0,27,55,73],"analyze":[1],"the":[2,13,18,48,51,95,105],"set":[3,14,52],"of":[4,9,15,17,53,65,85,99],"increasingly":[5],"enumerable":[6],"additive":[7],"submonoids":[8],"R,":[10],"for":[11,33,50],"instance,":[12],"logarithms":[16],"positive":[19],"integers":[20],"with":[21,111],"respect":[22],"to":[23],"a":[24,62,66,70],"given":[25],"base.":[26],"call":[28],"them":[29],"$\u03c9$-monoids.":[30],"The":[31],"$\u03c9$-monoids":[32,81],"which":[34],"consecutive":[35],"elements":[36],"become":[37],"arbitrarily":[38],"close":[39],"are":[40,83,91,109],"called":[41],"tempered":[42,71,92],"monoids.":[43],"This":[44],"is,":[45],"in":[46],"particular,":[47],"case":[49],"logarithms.":[54],"show":[56,76],"that":[57,82,90],"any":[58],"$\u03c9$-monoid":[59],"is":[60],"either":[61],"scalar":[63],"multiple":[64],"numerical":[67,86],"semigroup":[68],"or":[69],"monoid.":[72],"will":[74],"also":[75],"how":[77],"we":[78],"can":[79],"differentiate":[80],"multiples":[84],"semigroups":[87],"from":[88,113],"those":[89],"monoids":[93],"by":[94],"size":[96],"and":[97,107],"commensurability":[98],"their":[100],"minimal":[101],"generating":[102],"sets.":[103],"All":[104],"definitions":[106],"results":[108],"illustrated":[110],"examples":[112],"music":[114],"theory.":[115]},"counts_by_year":[],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
