{"id":"https://openalex.org/W4382626455","doi":"https://doi.org/10.1007/s00182-023-00850-7","title":"Impartial games with decreasing Sprague\u2013Grundy function and their hypergraph compound","display_name":"Impartial games with decreasing Sprague\u2013Grundy function and their hypergraph compound","publication_year":2023,"publication_date":"2023-05-04","ids":{"openalex":"https://openalex.org/W4382626455","doi":"https://doi.org/10.1007/s00182-023-00850-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00182-023-00850-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00182-023-00850-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00182-023-00850-7.pdf","source":{"id":"https://openalex.org/S132210109","display_name":"International Journal of Game Theory","issn_l":"0020-7276","issn":["0020-7276","1432-1270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Game Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00182-023-00850-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057621825","display_name":"Endre Boros","orcid":"https://orcid.org/0000-0001-8206-3168"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Endre Boros","raw_affiliation_strings":["MSIS and RUTCOR, RBS, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, USA"],"affiliations":[{"raw_affiliation_string":"MSIS and RUTCOR, RBS, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027250769","display_name":"Vladimir Gurvich","orcid":"https://orcid.org/0000-0002-8976-3527"},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir Gurvich","raw_affiliation_strings":["National Research University Higher School of Economics, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"National Research University Higher School of Economics, Moscow, Russia","institution_ids":["https://openalex.org/I118501908"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034387346","display_name":"Nhan Bao Ho","orcid":"https://orcid.org/0000-0002-6501-5495"},"institutions":[{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Nhan Bao Ho","raw_affiliation_strings":["Department of Mathematics and Statistics, La Trobe University, Melbourne, 3086, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, La Trobe University, Melbourne, 3086, Australia","institution_ids":["https://openalex.org/I196829312"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110768204","display_name":"Kazuhisa Makino","orcid":"https://orcid.org/0009-0000-9771-4955"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhisa Makino","raw_affiliation_strings":["Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, 606-8502, Japan"],"affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto, 606-8502, Japan","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084403476","display_name":"Peter Mur\u0161i\u010d","orcid":"https://orcid.org/0000-0002-7350-6809"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Peter Mursic","raw_affiliation_strings":["MSIS and RUTCOR, RBS, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, USA"],"affiliations":[{"raw_affiliation_string":"MSIS and RUTCOR, RBS, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5034387346"],"corresponding_institution_ids":["https://openalex.org/I196829312"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.5139,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70656591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"53","issue":"4","first_page":"1119","last_page":"1144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9983000159263611,"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":0.9983000159263611,"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/T11674","display_name":"Sports Analytics and Performance","score":0.9674000144004822,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11197","display_name":"Digital Games and Media","score":0.906499981880188,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.9873603582382202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.604668378829956},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.542312502861023},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5408052206039429},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5196184515953064},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45177170634269714},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.43929746747016907},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.43621906638145447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38187623023986816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24973627924919128},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.17911893129348755},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.054167240858078}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.9873603582382202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.604668378829956},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.542312502861023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5408052206039429},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5196184515953064},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45177170634269714},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.43929746747016907},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.43621906638145447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38187623023986816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24973627924919128},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.17911893129348755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.054167240858078},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00182-023-00850-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00182-023-00850-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00182-023-00850-7.pdf","source":{"id":"https://openalex.org/S132210109","display_name":"International Journal of Game Theory","issn_l":"0020-7276","issn":["0020-7276","1432-1270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Game Theory","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jogath:v:53:y:2024:i:4:d:10.1007_s00182-023-00850-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00182-023-00850-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":{"id":"doi:10.1007/s00182-023-00850-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00182-023-00850-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00182-023-00850-7.pdf","source":{"id":"https://openalex.org/S132210109","display_name":"International Journal of Game Theory","issn_l":"0020-7276","issn":["0020-7276","1432-1270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Game Theory","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G4854617120","display_name":null,"funder_award_id":"5-100","funder_id":"https://openalex.org/F4320324261","funder_display_name":"National Research University Higher School of Economics"},{"id":"https://openalex.org/G5786340949","display_name":null,"funder_award_id":"KAKENHI Grant Number","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5822131296","display_name":null,"funder_award_id":"19K22841","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6662511893","display_name":null,"funder_award_id":"20H00609","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G942612037","display_name":null,"funder_award_id":"20H05967","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320577","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27"},{"id":"https://openalex.org/F4320324261","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4382626455.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1976534581","https://openalex.org/W2037000885","https://openalex.org/W2068795011","https://openalex.org/W2114616381","https://openalex.org/W2317309498","https://openalex.org/W2328338920","https://openalex.org/W2330301979","https://openalex.org/W2401610261","https://openalex.org/W2481955307","https://openalex.org/W2917125947","https://openalex.org/W2962794564","https://openalex.org/W2963653532","https://openalex.org/W2979157816","https://openalex.org/W3001890424","https://openalex.org/W3159034505","https://openalex.org/W4213277361","https://openalex.org/W4233756358"],"related_works":["https://openalex.org/W2355730523","https://openalex.org/W4376608589","https://openalex.org/W152021879","https://openalex.org/W1537073411","https://openalex.org/W1948107826","https://openalex.org/W3138003926","https://openalex.org/W2072918937","https://openalex.org/W1630514295","https://openalex.org/W4300037846","https://openalex.org/W4288275998"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Sprague\u2013Grundy":[2],"(SG)":[3],"theory":[4],"reduces":[5],"the":[6,13,46,75,85],"disjunctive":[7],"compound":[8,76,88],"of":[9,16,27,53,59,89,117],"impartial":[10,28,31],"games":[11,55,72,92],"to":[12,56,108],"classical":[14],"game":[15,32],"NIM":[17,61,91],".":[18],"We":[19,63,97],"generalize":[20],"this":[21,66],"concept":[22],"by":[23,42],"introducing":[24],"hypergraph":[25,51,57,80,87,107],"compounds":[26,52,58],"games.":[29,62],"An":[30],"is":[33,40,81,93],"called":[34,82],"SG-decreasing":[35,54,83,95],"if":[36,70,84],"its":[37],"SG":[38,47],"value":[39],"decreased":[41],"every":[43],"move.":[44],"Extending":[45],"theory,":[48],"we":[49,122],"reduce":[50],"single-pile":[60,90],"show":[64],"that":[65],"reduction":[67],"works":[68],"only":[69],"all":[71],"involved":[73],"in":[74,130],"are":[77],"SG-decreasing.":[78,110],"A":[79],"corresponding":[86],"an":[94],"game.":[96],"provide":[98],"some":[99,102],"necessary":[100,125],"and":[101,126],"sufficient":[103,127],"conditions":[104],"for":[105,113],"a":[106,124],"be":[109],"In":[111],"particular,":[112],"hypergraphs":[114],"with":[115],"hyperedges":[116],"size":[118],"at":[119],"most":[120],"3":[121],"obtain":[123],"condition":[128],"verifiable":[129],"polynomial":[131],"time.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}