{"id":"https://openalex.org/W2062358873","doi":"https://doi.org/10.1137/0219077","title":"Computing Puiseux-Series Solutions to Determinantal Equations via Combinatorial Relaxation","display_name":"Computing Puiseux-Series Solutions to Determinantal Equations via Combinatorial Relaxation","publication_year":1990,"publication_date":"1990-12-01","ids":{"openalex":"https://openalex.org/W2062358873","doi":"https://doi.org/10.1137/0219077","mag":"2062358873"},"language":"en","primary_location":{"id":"doi:10.1137/0219077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219077","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5032957138","display_name":"Kazuo Murota","orcid":"https://orcid.org/0000-0003-1518-9152"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kazuo Murota","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032957138"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4806,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.63023223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"6","first_page":"1132","last_page":"1161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9937999844551086,"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":0.9937999844551086,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9653000235557556,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9442999958992004,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7447249889373779},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7252674102783203},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6002153754234314},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.5569655895233154},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.48902377486228943},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46001243591308594},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4481998383998871},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4177912473678589},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3335545063018799},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12854117155075073}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7447249889373779},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7252674102783203},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6002153754234314},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5569655895233154},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.48902377486228943},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46001243591308594},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4481998383998871},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4177912473678589},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3335545063018799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12854117155075073},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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:10.1137/0219077","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219077","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":18,"referenced_works":["https://openalex.org/W1564725221","https://openalex.org/W1971057413","https://openalex.org/W1998294324","https://openalex.org/W2004488477","https://openalex.org/W2029317328","https://openalex.org/W2031629670","https://openalex.org/W2046133214","https://openalex.org/W2048285065","https://openalex.org/W2056178482","https://openalex.org/W2073264848","https://openalex.org/W2125690626","https://openalex.org/W2500540229","https://openalex.org/W2612136303","https://openalex.org/W4232715883","https://openalex.org/W4233558979","https://openalex.org/W4299544197","https://openalex.org/W4301216918","https://openalex.org/W4301459590"],"related_works":["https://openalex.org/W1993426457","https://openalex.org/W2372176563","https://openalex.org/W2068949639","https://openalex.org/W3023620486","https://openalex.org/W4254345474","https://openalex.org/W2369485329","https://openalex.org/W4389457727","https://openalex.org/W1993206725","https://openalex.org/W2390916851","https://openalex.org/W1569384655"],"abstract_inverted_index":{"Let":[0],"$A(t,x)":[1],"=":[2,33,40],"(A_{ij}":[3],"(t,x))$":[4],"be":[5],"a":[6,12,64],"square":[7],"matrix":[8],"with":[9,59,68],"$A_{ij}$":[10],"being":[11],"polynomial":[13],"in":[14],"t":[15],"and":[16],"x.":[17],"This":[18],"paper":[19],"proposes":[20],"an":[21,47],"algorithm":[22,43,71],"for":[23,55],"computing":[24],"the":[25,36,51,60],"Puiseux":[26],"(=":[27],"fractional":[28],"power)":[29],"series":[30],"solutions":[31],"$x":[32],"x(t)$":[34],"to":[35],"equation":[37],"${\\operatorname{det}}A(t,":[38,57],"x)":[39],"0$.":[41],"The":[42,70],"is":[44,72],"based":[45],"on":[46],"observation":[48],"which":[49],"links":[50],"Newton":[52],"diagram":[53],"(polygon)":[54],"det":[56],"x)$":[58],"perfect":[61],"matchings":[62],"of":[63,77],"bipartite":[65],"graph":[66],"associated":[67],"A.":[69],"efficient,":[73],"making":[74],"full":[75],"use":[76],"available":[78],"fast":[79],"network-type":[80],"algorithms.":[81]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
