{"id":"https://openalex.org/W4362699093","doi":"https://doi.org/10.37236/11332","title":"A New Feasibility Condition for the AT4 Family","display_name":"A New Feasibility Condition for the AT4 Family","publication_year":2023,"publication_date":"2023-04-07","ids":{"openalex":"https://openalex.org/W4362699093","doi":"https://doi.org/10.37236/11332"},"language":"en","primary_location":{"id":"doi:10.37236/11332","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11332","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p7/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/v30i2p7/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069196389","display_name":"Zheng-Jiang Xia","orcid":"https://orcid.org/0000-0002-0173-3631"},"institutions":[{"id":"https://openalex.org/I188935350","display_name":"Anhui University of Finance and Economics","ror":"https://ror.org/0152zzg30","country_code":"CN","type":"education","lineage":["https://openalex.org/I188935350"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zheng-Jiang Xia","raw_affiliation_strings":["School of Finance, Anhui University of Finance & Economics, Bengbu, 233030, China"],"affiliations":[{"raw_affiliation_string":"School of Finance, Anhui University of Finance & Economics, Bengbu, 233030, China","institution_ids":["https://openalex.org/I188935350"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100331202","display_name":"Jae-Ho Lee","orcid":"https://orcid.org/0000-0002-5676-8612"},"institutions":[{"id":"https://openalex.org/I11874761","display_name":"University of North Florida","ror":"https://ror.org/01j903a45","country_code":"US","type":"education","lineage":["https://openalex.org/I11874761"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jae-Ho Lee","raw_affiliation_strings":["Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA","institution_ids":["https://openalex.org/I11874761"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048096758","display_name":"Jack H. Koolen","orcid":"https://orcid.org/0000-0002-8623-5681"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jack H. Koolen","raw_affiliation_strings":["CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui, 230026, PR China","School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, PR China"],"affiliations":[{"raw_affiliation_string":"CAS Wu Wen-Tsun Key Laboratory of Mathematics, University of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, PR China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069196389"],"corresponding_institution_ids":["https://openalex.org/I188935350"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9970999956130981,"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/T11476","display_name":"Graph theory and applications","score":0.9337999820709229,"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/T11130","display_name":"Coding theory and cryptography","score":0.9083999991416931,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/antipodal-point","display_name":"Antipodal point","score":0.9442921876907349},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.815718412399292},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8018887042999268},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6088178157806396},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5268368124961853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1595226228237152},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.141677588224411}],"concepts":[{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.9442921876907349},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.815718412399292},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8018887042999268},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6088178157806396},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5268368124961853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1595226228237152},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.141677588224411},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11332","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11332","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p7/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:10.37236/11332","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11332","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p7/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/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1557570493","display_name":null,"funder_award_id":"KJ2020A0015","funder_id":"https://openalex.org/F4320326664","funder_display_name":"Anhui Provincial Department of Education"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2121191339","display_name":null,"funder_award_id":"50000","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4548025536","display_name":null,"funder_award_id":"120714","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5167091242","display_name":null,"funder_award_id":"No. 1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5760752404","display_name":null,"funder_award_id":"Projects","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5797785011","display_name":null,"funder_award_id":"16010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6657395339","display_name":null,"funder_award_id":"12071454","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6729972075","display_name":null,"funder_award_id":"2018A04","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G925363208","display_name":null,"funder_award_id":"11601002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326664","display_name":"Anhui Provincial Department of Education","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4362699093.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W61123192","https://openalex.org/W1980184848","https://openalex.org/W2043758575","https://openalex.org/W2055484385","https://openalex.org/W2065738186","https://openalex.org/W2071884979","https://openalex.org/W2088550857","https://openalex.org/W2095808043","https://openalex.org/W2952268356","https://openalex.org/W3127307976","https://openalex.org/W4248395893","https://openalex.org/W4298236575","https://openalex.org/W6616784344"],"related_works":["https://openalex.org/W4390723618","https://openalex.org/W257437400","https://openalex.org/W2161334253","https://openalex.org/W4252046870","https://openalex.org/W2126408028","https://openalex.org/W2040722700","https://openalex.org/W4255081583","https://openalex.org/W2980963558","https://openalex.org/W16605181","https://openalex.org/W150815011"],"abstract_inverted_index":{"Let":[0],"$\\Gamma$":[1,14,30,43,51,74],"be":[2,117],"an":[3,80,118],"antipodal":[4,68,81,119],"distance-regular":[5],"graph":[6,83],"with":[7,35,87,140],"diameter":[8,85],"$4$":[9,86],"and":[10,23,39,59,77,107],"eigenvalues":[11,37],"$\\theta_0>\\theta_1>\\theta_2>\\theta_3>\\theta_4$.":[12],"Then":[13,46],"is":[15,31,44,63],"tight":[16,82,120],"in":[17,54],"the":[18,47,64,67,100,111,137],"sense":[19],"of":[20,50,56,66,70,84,114],"Juri\u0161i\u0107,":[21],"Koolen,":[22],"Terwilliger":[24],"(J.":[25],"Algebraic":[26],"Combin,":[27],"2000)":[28],"whenever":[29],"locally":[32],"strongly":[33],"regular":[34],"nontrivial":[36],"$p:=\\theta_2$":[38],"$-q:=\\theta_3$.":[40],"Assume":[41],"that":[42,126],"tight.":[45],"intersection":[48],"numbers":[49],"are":[52],"expressed":[53],"terms":[55],"$p$,":[57],"$q$,":[58],"$r$,":[60],"where":[61],"$r$":[62],"size":[65],"classes":[69],"$\\Gamma$.":[71],"We":[72,103,135],"denote":[73],"by":[75],"$\\mathrm{AT4}(p,q,r)$":[76,101,138],"call":[78],"this":[79,91,122],"parameters":[88],"$p,q,r$.":[89],"In":[90],"paper,":[92],"we":[93,124],"give":[94],"a":[95,105],"new":[96],"feasibility":[97],"condition":[98,109],"for":[99,110,132],"family.":[102],"determine":[104],"necessary":[106],"sufficient":[108],"second":[112],"subconstituent":[113],"$\\mathrm{AT4}(p,q,2)$":[115],"to":[116],"graph.Using":[121],"condition,":[123],"prove":[125],"there":[127],"does":[128],"not":[129],"exist":[130],"$\\mathrm{AT4}(q^3-2q,q,2)$":[131],"$q\\equiv3$":[133],"$(\\mathrm{mod}~4)$.":[134],"discuss":[136],"graphs":[139],"$r=(p+q^3)(p+q)^{-1}$.":[141]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}