{"id":"https://openalex.org/W2963525843","doi":"https://doi.org/10.37236/3260","title":"Characterizations of Regularity for certain $Q$-Polynomial Association Schemes","display_name":"Characterizations of Regularity for certain $Q$-Polynomial Association Schemes","publication_year":2015,"publication_date":"2015-01-20","ids":{"openalex":"https://openalex.org/W2963525843","doi":"https://doi.org/10.37236/3260","mag":"2963525843"},"language":"en","primary_location":{"id":"doi:10.37236/3260","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3260","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p12/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p12/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036298064","display_name":"Sho Suda","orcid":"https://orcid.org/0000-0002-5280-2668"},"institutions":[{"id":"https://openalex.org/I39018119","display_name":"Aichi University of Education","ror":"https://ror.org/03m964n84","country_code":"JP","type":"education","lineage":["https://openalex.org/I39018119"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Sho Suda","raw_affiliation_strings":["Aichi University of Education"],"affiliations":[{"raw_affiliation_string":"Aichi University of Education","institution_ids":["https://openalex.org/I39018119"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036298064"],"corresponding_institution_ids":["https://openalex.org/I39018119"],"apc_list":null,"apc_paid":null,"fwci":0.4451,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80918555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9991000294685364,"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/T10849","display_name":"Finite Group Theory Research","score":0.9962999820709229,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/association-scheme","display_name":"Association scheme","score":0.8787837028503418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7980703115463257},{"id":"https://openalex.org/keywords/mutually-unbiased-bases","display_name":"Mutually unbiased bases","score":0.665490984916687},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5930157899856567},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5922993421554565},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5656117796897888},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5572053790092468},{"id":"https://openalex.org/keywords/association","display_name":"Association (psychology)","score":0.4564741253852844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41172122955322266},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30300042033195496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12441709637641907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05251321196556091},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.04494333267211914}],"concepts":[{"id":"https://openalex.org/C73361133","wikidata":"https://www.wikidata.org/wiki/Q4810150","display_name":"Association scheme","level":2,"score":0.8787837028503418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7980703115463257},{"id":"https://openalex.org/C158587675","wikidata":"https://www.wikidata.org/wiki/Q17160413","display_name":"Mutually unbiased bases","level":3,"score":0.665490984916687},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5930157899856567},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5922993421554565},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5656117796897888},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5572053790092468},{"id":"https://openalex.org/C142853389","wikidata":"https://www.wikidata.org/wiki/Q744778","display_name":"Association (psychology)","level":2,"score":0.4564741253852844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41172122955322266},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30300042033195496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12441709637641907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05251321196556091},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.04494333267211914},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3260","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3260","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p12/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"}],"best_oa_location":{"id":"doi:10.37236/3260","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3260","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p12/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":[{"id":"https://openalex.org/G1523731414","display_name":null,"funder_award_id":"Research Fellowships for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5640883929","display_name":null,"funder_award_id":"Research Fellow","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8004478673","display_name":null,"funder_award_id":"JSPS Research Fellowship","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8470055433","display_name":null,"funder_award_id":"Research Fellowship","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8485472354","display_name":null,"funder_award_id":"JSPS Research Fellow","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G942918087","display_name":null,"funder_award_id":"JSPS Research Fellowships for Young Scientists","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"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/W2963525843.pdf","grobid_xml":"https://content.openalex.org/works/W2963525843.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W109405981","https://openalex.org/W1551490643","https://openalex.org/W1581293664","https://openalex.org/W1985211463","https://openalex.org/W2046462163","https://openalex.org/W2067432723","https://openalex.org/W2080403200","https://openalex.org/W2085419283","https://openalex.org/W2142915235","https://openalex.org/W2584020404","https://openalex.org/W3021878526","https://openalex.org/W3123882671","https://openalex.org/W6604019045","https://openalex.org/W6634642888"],"related_works":["https://openalex.org/W4229705064","https://openalex.org/W2054051424","https://openalex.org/W599879082","https://openalex.org/W2096095878","https://openalex.org/W1539726851","https://openalex.org/W2963525843","https://openalex.org/W2142915235","https://openalex.org/W4362606175","https://openalex.org/W1578994341","https://openalex.org/W2952816677"],"abstract_inverted_index":{"It":[0],"was":[1],"shown":[2],"that":[3,41],"linked":[4,29],"systems":[5,30],"of":[6,28,31,45,58],"symmetric":[7,32],"designs":[8,33],"with":[9],"$a_1^*=0$":[10],"and":[11,53],"mutually":[12],"unbiased":[13],"bases":[14],"(MUBs)":[15],"are":[16],"triply":[17],"regular":[18,50],"association":[19,51],"schemes.":[20],"In":[21],"this":[22],"paper,":[23],"we":[24,39],"characterize":[25,54],"triple":[26],"regularity":[27,57],"by":[34,60],"its":[35,61],"Krein":[36],"number.":[37],"And":[38],"prove":[40],"a":[42,48],"maximal":[43],"set":[44],"MUBs":[46,59],"carries":[47],"quadruply":[49],"scheme":[52],"the":[55],"quadruple":[56],"parameter.":[62]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}