{"id":"https://openalex.org/W2519096471","doi":"https://doi.org/10.3233/fi-2016-1377","title":"Congruences of Edge-bipartite Graphs with Applications to Grothendieck Group Recognition I. Inflation Algorithm Revisited*","display_name":"Congruences of Edge-bipartite Graphs with Applications to Grothendieck Group Recognition I. Inflation Algorithm Revisited*","publication_year":2016,"publication_date":"2016-09-13","ids":{"openalex":"https://openalex.org/W2519096471","doi":"https://doi.org/10.3233/fi-2016-1377","mag":"2519096471"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2016-1377","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1377","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5011873433","display_name":"Andrzej Mr\u00f3z","orcid":"https://orcid.org/0000-0002-4337-7313"},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej Mr\u00f3z","raw_affiliation_strings":["Centro de Investigaci\u00f3n en Matem\u00e1ticas, A.C., Jalisco S/N, Col. Valenciana CP: 36023 Guanajuato, Gto, Mexico, and Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Investigaci\u00f3n en Matem\u00e1ticas, A.C., Jalisco S/N, Col. Valenciana CP: 36023 Guanajuato, Gto, Mexico, and Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011873433"],"corresponding_institution_ids":["https://openalex.org/I3019271933"],"apc_list":null,"apc_paid":null,"fwci":8.349,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.98120228,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"146","issue":"2","first_page":"121","last_page":"144"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7411909103393555},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6456210613250732},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.581216037273407},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5039069056510925},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42054474353790283},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39269566535949707},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36671531200408936},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.22795620560646057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7411909103393555},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6456210613250732},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.581216037273407},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5039069056510925},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42054474353790283},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39269566535949707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36671531200408936},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.22795620560646057},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2016-1377","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1377","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.5699999928474426,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W934221954","https://openalex.org/W965483201","https://openalex.org/W1261728726","https://openalex.org/W1480516528","https://openalex.org/W1487444668","https://openalex.org/W1548384067","https://openalex.org/W1553753142","https://openalex.org/W1565930783","https://openalex.org/W1601437069","https://openalex.org/W1633885552","https://openalex.org/W1649048995","https://openalex.org/W1976264037","https://openalex.org/W1981881356","https://openalex.org/W1984299062","https://openalex.org/W1989125084","https://openalex.org/W1993013780","https://openalex.org/W2003354322","https://openalex.org/W2014289472","https://openalex.org/W2017014095","https://openalex.org/W2025140234","https://openalex.org/W2028449252","https://openalex.org/W2052546549","https://openalex.org/W2058259340","https://openalex.org/W2064529159","https://openalex.org/W2093076141","https://openalex.org/W2187425528","https://openalex.org/W2304308747","https://openalex.org/W2345501689","https://openalex.org/W2346769286","https://openalex.org/W2418172795","https://openalex.org/W2521001849","https://openalex.org/W2604988676"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2371352078","https://openalex.org/W4394650907","https://openalex.org/W154364797","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W4390409907","https://openalex.org/W2586280130","https://openalex.org/W4221143622"],"abstract_inverted_index":{"We":[0,81,101],"study":[1],"edge-bipartite":[2],"graphs":[3],"(bigraphs),":[4],"a":[5,24,104,145,149,152,158],"class":[6],"of":[7,12,52,57,70,85,92,112,117,125,129,148,151,154,166,180],"signed":[8],"graphs,":[9],"by":[10,49],"means":[11],"the":[13,31,86,107,118,139,142,186],"inflation":[14,87,113],"algorithm":[15,88],"which":[16,174],"relies":[17],"on":[18,23,30],"performing":[19],"certain":[20],"elementary":[21],"transformations":[22],"given":[25],"bigraph":[26],"\u0394,":[27],"or":[28],"equivalently,":[29],"associated":[32],"integral":[33,71],"quadratic":[34,72,130],"form":[35],"q\u0394":[36],":":[37],"\u2124n":[38],"\u2192":[39],"\u2124,":[40],"preserving":[41],"Gram":[42],"\u2124-congruence.":[43],"The":[44],"idea":[45],"s":[46],"are":[47,144],"inspired":[48],"classical":[50],"results":[51,143],"Ovsienko":[53],"and":[54,73,76,89,97,109,132,170],"recent":[55],"studies":[56],"Simson":[58],"started":[59],"in":[60,103,163,177],"[SIAM":[61],"J.":[62],"Discr.":[63],"Math.":[64],"27":[65],"(2013),":[66],"827-854],":[67],"concerning":[68],"classifications":[69],"bilinear":[74],"forms,":[75],"their":[77,133,171],"Coxeter":[78],"spectral":[79],"analysis.":[80],"provide":[82],"few":[83],"modifications":[84],"new":[90],"estimations":[91],"its":[93],"complexity":[94],"for":[95],"positive":[96],"principal":[98],"loop-free":[99],"bigraphs.":[100],"discuss":[102,176],"systematic":[105],"way":[106],"behavior":[108],"computational":[110],"aspects":[111],"techniques.":[114],"As":[115],"one":[116],"consequences":[119],"we":[120,175],"obtain":[121],"relatively":[122],"simple":[123],"proofs":[124],"several":[126],"interesting":[127],"properties":[128],"forms":[131],"roots,":[134],"extending":[135],"known":[136],"facts.":[137],"On":[138],"other":[140],"hand,":[141],"first":[146],"step":[147],"solution":[150],"variant":[153],"Grothendieck":[155],"group":[156],"recognition,":[157],"difficult":[159],"combinatorial":[160],"problem":[161],"arising":[162],"representation":[164],"theory":[165],"finite":[167],"dimensional":[168],"algebras":[169],"derived":[172],"categories,":[173],"Part":[178],"II":[179],"this":[181],"two":[182],"parts":[183],"article":[184],"with":[185],"same":[187],"main":[188],"title.":[189]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
