{"id":"https://openalex.org/W1495329404","doi":"https://doi.org/10.37236/2082","title":"A Dice Rolling Game on a Set of Tori","display_name":"A Dice Rolling Game on a Set of Tori","publication_year":2012,"publication_date":"2012-03-09","ids":{"openalex":"https://openalex.org/W1495329404","doi":"https://doi.org/10.37236/2082","mag":"1495329404"},"language":"en","primary_location":{"id":"doi:10.37236/2082","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2082","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p54/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p54/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078763719","display_name":"Jeehoon Kang","orcid":"https://orcid.org/0000-0002-2115-0871"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jeehoon Kang","raw_affiliation_strings":["Seoul National University","Seoul National Univ"],"affiliations":[{"raw_affiliation_string":"Seoul National University","institution_ids":["https://openalex.org/I139264467"]},{"raw_affiliation_string":"Seoul National Univ","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048188662","display_name":"Suh-Ryung Kim","orcid":"https://orcid.org/0000-0002-3296-7676"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Suh-Ryung Kim","raw_affiliation_strings":["Seoul National University","Seoul National Univ"],"affiliations":[{"raw_affiliation_string":"Seoul National University","institution_ids":["https://openalex.org/I139264467"]},{"raw_affiliation_string":"Seoul National Univ","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101459574","display_name":"Boram Park","orcid":"https://orcid.org/0000-0003-4102-1206"},"institutions":[{"id":"https://openalex.org/I2799411422","display_name":"Center for Discrete Mathematics and Theoretical Computer Science","ror":"https://ror.org/00k551w06","country_code":"US","type":"facility","lineage":["https://openalex.org/I102322142","https://openalex.org/I118347220","https://openalex.org/I1283103587","https://openalex.org/I1311060795","https://openalex.org/I20089843","https://openalex.org/I2799411422","https://openalex.org/I4210107353"]},{"id":"https://openalex.org/I4210096112","display_name":"Rutgers Sexual and Reproductive Health and Rights","ror":"https://ror.org/00rcvgx40","country_code":"NL","type":"other","lineage":["https://openalex.org/I4210096112"]},{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["NL","US"],"is_corresponding":false,"raw_author_name":"Boram Park","raw_affiliation_strings":["DIMACS, Rutgers University","DIMACS/Rutgers University"],"affiliations":[{"raw_affiliation_string":"DIMACS, Rutgers University","institution_ids":["https://openalex.org/I2799411422","https://openalex.org/I102322142","https://openalex.org/I4210096112"]},{"raw_affiliation_string":"DIMACS/Rutgers University","institution_ids":["https://openalex.org/I2799411422","https://openalex.org/I102322142","https://openalex.org/I4210096112"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078763719"],"corresponding_institution_ids":["https://openalex.org/I139264467"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03893578,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9740999937057495,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9740999937057495,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9677000045776367,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.965399980545044,"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/mathematics","display_name":"Mathematics","score":0.7824829816818237},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5359014272689819},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5357481837272644},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.5194963216781616},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.5040292143821716},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.47619664669036865},{"id":"https://openalex.org/keywords/commutative-algebra","display_name":"Commutative algebra","score":0.4718335270881653},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4609004259109497},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.45762547850608826},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.43465954065322876},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43117856979370117},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42798030376434326},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3065197467803955}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7824829816818237},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5359014272689819},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5357481837272644},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.5194963216781616},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.5040292143821716},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.47619664669036865},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.4718335270881653},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4609004259109497},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.45762547850608826},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.43465954065322876},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43117856979370117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42798030376434326},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3065197467803955},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2082","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2082","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p54/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/2082","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2082","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p54/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2792016499","display_name":null,"funder_award_id":"NRF-2011-357-C00004","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"},{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G3942910960","display_name":null,"funder_award_id":"(NRF) grant","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G6152606782","display_name":null,"funder_award_id":"2011-3","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"},{"id":"https://openalex.org/G626505518","display_name":null,"funder_award_id":"No. 201","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G7335014400","display_name":null,"funder_award_id":"2011-3","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G982292920","display_name":null,"funder_award_id":"NRF-20","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1495329404.pdf","grobid_xml":"https://content.openalex.org/works/W1495329404.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1975858062"],"related_works":["https://openalex.org/W4308298797","https://openalex.org/W4255963200","https://openalex.org/W2360590989","https://openalex.org/W4255391830","https://openalex.org/W2369074270","https://openalex.org/W2408222820","https://openalex.org/W2741158649","https://openalex.org/W2253391970","https://openalex.org/W2953844587","https://openalex.org/W1565509971"],"abstract_inverted_index":{"Some":[0],"linear":[1,52,154],"algebraic":[2],"and":[3,48,95,124,146],"combinatorial":[4,63],"problems":[5],"are":[6],"widely":[7],"studied":[8],"in":[9,25,85,98,103,142],"connection":[10],"with":[11],"$\\sigma$-games.":[12],"One":[13],"particularissue":[14],"is":[15,90,135],"to":[16,115,136],"characterize":[17,117],"whether":[18],"or":[19],"not":[20],"a":[21,33,37,111,126,149],"given":[22,34,150],"vector":[23],"lies":[24],"the":[26,30,51,59,91,106,118,133,143,153],"submodule":[27,119],"generated":[28,120],"by":[29,93,121],"rows":[31,123],"of":[32,75,88,100,156],"matrix":[35,60,112],"over":[36,54,113],"commutative":[38,55],"ring.":[39,56],"In":[40,105],"general,":[41],"one":[42,65],"can":[43,71],"solve":[44],"this":[45,86],"problem":[46],"easily":[47],"algorithmically":[49],"using":[50],"algebra":[53],"However,":[57],"if":[58],"has":[61],"some":[62,69,161],"structure,":[64],"may":[66],"expect":[67],"that":[68],"more":[70],"be":[72],"asserted":[73],"instead":[74],"merely":[76],"giving":[77],"an":[78],"algorithm.":[79],"A":[80],"recent":[81],"outstanding":[82],"example":[83],"appeared":[84],"line":[87],"research":[89],"paper":[92],"Florence":[94],"Meunier":[96],"published":[97],"Journal":[99],"Algebraic":[101],"Combinatorics":[102],"2010.":[104],"same":[107],"spirit,":[108],"we":[109],"consider":[110],"$\\mathbb{Z}_n$":[114],"completely":[116],"its":[122],"give":[125],"constructive":[127],"proof.":[128],"The":[129],"main":[130],"idea":[131],"for":[132],"characterization":[134],"find":[137],"certain":[138],"good":[139],"basic":[140],"elements":[141],"row":[144],"space":[145],"then":[147],"express":[148],"element":[151],"as":[152,158,160],"combination":[155],"them":[157],"well":[159],"additional":[162],"term.":[163]},"counts_by_year":[],"updated_date":"2026-03-14T08:43:22.919905","created_date":"2025-10-10T00:00:00"}
