{"id":"https://openalex.org/W3088307503","doi":"https://doi.org/10.1080/00029890.2020.1785254","title":"Numerical Semigroups and the Game of Sylver Coinage","display_name":"Numerical Semigroups and the Game of Sylver Coinage","publication_year":2020,"publication_date":"2020-09-13","ids":{"openalex":"https://openalex.org/W3088307503","doi":"https://doi.org/10.1080/00029890.2020.1785254","mag":"3088307503"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1785254","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1785254","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":"article","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/A5035894323","display_name":"Rachel Eaton","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089612","display_name":"United States Air Force","ror":"https://ror.org/006gmme17","country_code":"US","type":"funder","lineage":["https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105"]},{"id":"https://openalex.org/I893718555","display_name":"Joint Base San Antonio","ror":"https://ror.org/02jxznk77","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I893718555"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rachel Eaton","raw_affiliation_strings":["United States Air Force, Lackland AFB, San Antonio, TX 78242;"],"affiliations":[{"raw_affiliation_string":"United States Air Force, Lackland AFB, San Antonio, TX 78242;","institution_ids":["https://openalex.org/I893718555","https://openalex.org/I4210089612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001321482","display_name":"Kurt Herzinger","orcid":null},"institutions":[{"id":"https://openalex.org/I430641","display_name":"United States Air Force Academy","ror":"https://ror.org/0055d0g64","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I430641"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kurt Herzinger","raw_affiliation_strings":["United States Air Force Academy, USAFA, Colorado Springs, CO 80840;"],"affiliations":[{"raw_affiliation_string":"United States Air Force Academy, USAFA, Colorado Springs, CO 80840;","institution_ids":["https://openalex.org/I430641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080714700","display_name":"Ian Pierce","orcid":null},"institutions":[{"id":"https://openalex.org/I430641","display_name":"United States Air Force Academy","ror":"https://ror.org/0055d0g64","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I430641"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ian Pierce","raw_affiliation_strings":["United States Air Force Academy, USAFA, Colorado Springs, CO 80840;"],"affiliations":[{"raw_affiliation_string":"United States Air Force Academy, USAFA, Colorado Springs, CO 80840;","institution_ids":["https://openalex.org/I430641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003319003","display_name":"Jeremy Thompson","orcid":"https://orcid.org/0000-0003-2980-0899"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeremy Thompson","raw_affiliation_strings":["Department of Applied Mathematics, University of Colorado, Boulder, CO 80309"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Colorado, Boulder, CO 80309","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5080714700"],"corresponding_institution_ids":["https://openalex.org/I430641"],"apc_list":null,"apc_paid":null,"fwci":0.1407,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53127041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"127","issue":"8","first_page":"706","last_page":"715"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9937000274658203,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9848999977111816,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cognitive-reframing","display_name":"Cognitive reframing","score":0.8110159635543823},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.7682439088821411},{"id":"https://openalex.org/keywords/numerical-semigroup","display_name":"Numerical semigroup","score":0.7219313979148865},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.7199671268463135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5515744090080261},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5424862504005432},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3362870216369629},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.32248473167419434},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2913873493671417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28929466009140015},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2890841066837311},{"id":"https://openalex.org/keywords/social-psychology","display_name":"Social psychology","score":0.10767024755477905},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.07148176431655884}],"concepts":[{"id":"https://openalex.org/C187029079","wikidata":"https://www.wikidata.org/wiki/Q958679","display_name":"Cognitive reframing","level":2,"score":0.8110159635543823},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7682439088821411},{"id":"https://openalex.org/C2779628518","wikidata":"https://www.wikidata.org/wiki/Q7069664","display_name":"Numerical semigroup","level":3,"score":0.7219313979148865},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.7199671268463135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5515744090080261},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5424862504005432},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3362870216369629},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32248473167419434},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2913873493671417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28929466009140015},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2890841066837311},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.10767024755477905},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.07148176431655884},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"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/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1785254","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1785254","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1980041466","https://openalex.org/W2017468867","https://openalex.org/W2053924765","https://openalex.org/W2318879138","https://openalex.org/W2320330683","https://openalex.org/W2332901121","https://openalex.org/W2894564506","https://openalex.org/W4237442181"],"related_works":["https://openalex.org/W2522074991","https://openalex.org/W2153946164","https://openalex.org/W2953366618","https://openalex.org/W4289919814","https://openalex.org/W3041033841","https://openalex.org/W4306979010","https://openalex.org/W2963027990","https://openalex.org/W4322760346","https://openalex.org/W2920530075","https://openalex.org/W2154197819"],"abstract_inverted_index":{"In":[0],"Conway\u2019s":[1],"game,":[2],"Sylver":[3,45,61,83,114],"Coinage,":[4],"the":[5,11,29,52,58,78,98],"set":[6],"of":[7,13,21,33,60,65,73,82,87,97,108],"legal":[8],"plays":[9],"forms":[10],"complement":[12],"a":[14,18,71,94],"numerical":[15,34,66,89],"semigroup":[16,90],"after":[17],"finite":[19],"number":[20,72],"turns.":[22],"Our":[23],"goal":[24],"is":[25],"to":[26,39,44,57],"show":[27],"how":[28,106],"tools":[30],"and":[31,54,80],"techniques":[32],"semigroups":[35],"can":[36],"be":[37,117],"brought":[38],"bear":[40],"on":[41],"questions":[42,112],"related":[43,56],"Coinage.":[46],"We":[47,102],"begin":[48],"by":[49,104],"formally":[50],"connecting":[51],"definitions":[53],"concepts":[55],"game":[59],"Coinage":[62,84,115],"with":[63,93],"those":[64],"semigroups.":[67],"Then":[68],"we":[69],"reframe":[70],"previously":[74],"known":[75],"results":[76],"about":[77,113],"play":[79],"strategy":[81],"in":[85],"terms":[86],"basic":[88],"theory,":[91],"culminating":[92],"semigroup-based":[95],"proof":[96],"quiet":[99],"end":[100],"theorem.":[101],"conclude":[103],"suggesting":[105],"several":[107],"R.":[109],"Guy\u2019s":[110],"twenty":[111],"may":[116],"approached":[118],"using":[119],"this":[120],"new":[121],"framework.":[122]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}