{"id":"https://openalex.org/W2043025681","doi":"https://doi.org/10.1007/pl00009832","title":"On Butler's Unimodality Result","display_name":"On Butler's Unimodality Result","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W2043025681","doi":"https://doi.org/10.1007/pl00009832","mag":"2043025681"},"language":"en","primary_location":{"id":"doi:10.1007/pl00009832","is_oa":false,"landing_page_url":"https://doi.org/10.1007/pl00009832","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"COMBINATORICA","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/A5040492103","display_name":"Yugen Takegahara","orcid":"https://orcid.org/0000-0002-2547-7070"},"institutions":[{"id":"https://openalex.org/I41725924","display_name":"Muroran Institute of Technology","ror":"https://ror.org/04rymkk69","country_code":"JP","type":"education","lineage":["https://openalex.org/I41725924"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yugen Takegahara","raw_affiliation_strings":["Muroran Institute of Technology; 27-1 Mizumoto, Muroran 050, Japan;","27-1 Mizumoto, Muroran 050, Japan","Muroran Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Muroran Institute of Technology; 27-1 Mizumoto, Muroran 050, Japan;","institution_ids":["https://openalex.org/I41725924"]},{"raw_affiliation_string":"27-1 Mizumoto, Muroran 050, Japan","institution_ids":[]},{"raw_affiliation_string":"Muroran Institute of Technology","institution_ids":["https://openalex.org/I41725924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040492103"],"corresponding_institution_ids":["https://openalex.org/I41725924"],"apc_list":null,"apc_paid":null,"fwci":1.0575,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76649864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"3","first_page":"437","last_page":"439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9750000238418579,"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/T12504","display_name":"Mathematics and Applications","score":0.9060999751091003,"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":0.9465682506561279},{"id":"https://openalex.org/keywords/unimodality","display_name":"Unimodality","score":0.8820217847824097},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7088223099708557},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6752150058746338},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6219244003295898},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5385452508926392},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.528506338596344},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4256698191165924},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34156641364097595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08576992154121399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9465682506561279},{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.8820217847824097},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7088223099708557},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6752150058746338},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6219244003295898},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5385452508926392},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.528506338596344},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4256698191165924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34156641364097595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08576992154121399},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/pl00009832","is_oa":false,"landing_page_url":"https://doi.org/10.1007/pl00009832","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"COMBINATORICA","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2373855227","https://openalex.org/W2010176972","https://openalex.org/W2075968040","https://openalex.org/W94338811","https://openalex.org/W4389974503","https://openalex.org/W2076454667","https://openalex.org/W27154759","https://openalex.org/W2054787334","https://openalex.org/W2096624034","https://openalex.org/W4382699971"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}