{"id":"https://openalex.org/W2998362283","doi":"https://doi.org/10.37236/9252","title":"Combinatorial Game Distributions of Steiner Systems","display_name":"Combinatorial Game Distributions of Steiner Systems","publication_year":2021,"publication_date":"2021-12-17","ids":{"openalex":"https://openalex.org/W2998362283","doi":"https://doi.org/10.37236/9252","mag":"2998362283"},"language":"en","primary_location":{"id":"doi:10.37236/9252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p54/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/v28i4p54/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038230907","display_name":"Yuki Irie","orcid":"https://orcid.org/0000-0002-6034-656X"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yuki Irie","raw_affiliation_strings":["Research Alliance Center for Mathematical Sciences, Tohoku University","Tohoku University (),"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Alliance Center for Mathematical Sciences, Tohoku University","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Tohoku University (),","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038230907"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":0.1399,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51244153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9921000003814697,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9921000003814697,"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/combinatorics","display_name":"Combinatorics","score":0.7708206176757812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6248239278793335},{"id":"https://openalex.org/keywords/steiner-system","display_name":"Steiner system","score":0.5355631709098816},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5101099610328674},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.45513853430747986},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.45476844906806946},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.4365411102771759},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41381973028182983},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.404536634683609},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14633804559707642}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7708206176757812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6248239278793335},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.5355631709098816},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5101099610328674},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45513853430747986},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.45476844906806946},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.4365411102771759},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41381973028182983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.404536634683609},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14633804559707642},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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":4,"locations":[{"id":"doi:10.37236/9252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p54/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:2001.00415","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.00415","pdf_url":"https://arxiv.org/pdf/2001.00415","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":null,"raw_type":"text"},{"id":"mag:2998362283","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2001.00415.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.2001.00415","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.00415","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/9252","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9252","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p54/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":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2998362283.pdf","grobid_xml":"https://content.openalex.org/works/W2998362283.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1979460411","https://openalex.org/W1981695594","https://openalex.org/W1991800073","https://openalex.org/W2009305829","https://openalex.org/W2075906776","https://openalex.org/W2080721903","https://openalex.org/W2090698102","https://openalex.org/W2099479910","https://openalex.org/W2114769645","https://openalex.org/W2261622378","https://openalex.org/W2894564506","https://openalex.org/W2994184532","https://openalex.org/W2995731717","https://openalex.org/W3013620999","https://openalex.org/W3197714832","https://openalex.org/W6645023723","https://openalex.org/W6652890618","https://openalex.org/W6671136405","https://openalex.org/W6677195681"],"related_works":["https://openalex.org/W1992526367","https://openalex.org/W2514085586","https://openalex.org/W2913086079","https://openalex.org/W3118514153","https://openalex.org/W1642923334","https://openalex.org/W3016715835","https://openalex.org/W2119414881","https://openalex.org/W3089739213","https://openalex.org/W3041462746","https://openalex.org/W2953974932","https://openalex.org/W2071891973","https://openalex.org/W2984916053","https://openalex.org/W1986500264","https://openalex.org/W2408525869","https://openalex.org/W3204399888","https://openalex.org/W1588146980","https://openalex.org/W2468944352","https://openalex.org/W1983124876","https://openalex.org/W229954229","https://openalex.org/W2555309099"],"abstract_inverted_index":{"The":[0],"$P$-position":[1,14,68,113],"sets":[2],"of":[3,16,30,139,161,170,173,190],"some":[4],"combinatorial":[5,9],"games":[6,46,176],"have":[7],"special":[8],"structures.":[10],"For":[11,58,102],"example,":[12],"the":[13,17,27,31,38,80,89,123,132,136,142,158,167,171,187],"set":[15,29,69,97,114],"hexad":[18,124],"game,":[19,125],"first":[20],"investigated":[21],"by":[22,42,153],"Conway":[23],"and":[24,126,203,212],"Ryba,":[25],"is":[26,70,115,129,166,209],"block":[28,72,117],"Steiner":[32,53,61,150,163,179,206],"system":[33,164,208],"$S(5,":[34,92,104],"6,":[35,93,105],"12)$":[36,94],"in":[37,55,175],"shuffle":[39],"numbering,":[40],"denoted":[41],"$D_{\\text{sh}}$.":[43],"However,":[44],"few":[45],"were":[47],"known":[48],"to":[49,52,182],"be":[50,198],"related":[51],"systems":[54,152,180],"this":[56,127],"way.":[57],"a":[59,65,110,162,205,219],"given":[60],"system,":[62],"we":[63,78,85,121,147],"construct":[64],"game":[66,111,128,134,155,159,188,216],"whose":[67,112],"its":[71,116,215],"set.":[73,118],"By":[74],"using":[75,154],"constructed":[76],"games,":[77],"obtain":[79,122],"following":[81],"two":[82],"results.":[83],"First,":[84],"characterize":[86,148],"$D_{\\text{sh}}$":[87],"among":[88,141],"5040":[90,144],"isomorphic":[91,181],"with":[95,135],"point":[96],"$\\{0,":[98],"1,":[99,195],"...,":[100],"11\\}$.":[101],"each":[103],"12)$,":[106],"our":[107],"construction":[108],"produces":[109],"From":[119],"$D_{\\text{sh}}$,":[120],"characterized":[130],"as":[131],"unique":[133,220],"minimum":[137],"number":[138],"positions":[140,174],"obtained":[143,177],"games.":[145],"Second,":[146],"projective":[149,210],"triple":[151,207],"distributions.":[156],"Here,":[157],"distribution":[160,169,189,217],"$D$":[165],"frequency":[168],"numbers":[172],"from":[178],"$D$.":[183],"We":[184],"find":[185],"that":[186,204],"an":[191],"$S(t,":[192],"t":[193],"+":[194],"v)$":[196],"can":[197],"decomposed":[199],"into":[200],"symmetric":[201,221],"components":[202],"if":[211,214],"only":[213],"has":[218],"component.":[222]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}