{"id":"https://openalex.org/W2127319721","doi":"https://doi.org/10.1155/2011/148580","title":"Group Divisible Designs with Two Associate Classes and <i>\u03bb</i><sub>2</sub> = 1","display_name":"Group Divisible Designs with Two Associate Classes and <i>\u03bb</i><sub>2</sub> = 1","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2127319721","doi":"https://doi.org/10.1155/2011/148580","mag":"2127319721"},"language":"en","primary_location":{"id":"doi:10.1155/2011/148580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/148580","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/148580.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2011/148580.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054255409","display_name":"Nittiya Pabhapote","orcid":null},"institutions":[{"id":"https://openalex.org/I129496196","display_name":"University of the Thai Chamber of Commerce","ror":"https://ror.org/03m7a5q02","country_code":"TH","type":"education","lineage":["https://openalex.org/I129496196"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Nittiya Pabhapote","raw_affiliation_strings":["Department of Mathematics, University of the Thai Chamber of Commerce, Dindaeng, Bangkok 10400, Thailand","University of the Thai Chamber of Commerce"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of the Thai Chamber of Commerce, Dindaeng, Bangkok 10400, Thailand","institution_ids":["https://openalex.org/I129496196"]},{"raw_affiliation_string":"University of the Thai Chamber of Commerce","institution_ids":["https://openalex.org/I129496196"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048240264","display_name":"Narong Punnim","orcid":null},"institutions":[{"id":"https://openalex.org/I76920116","display_name":"Srinakharinwirot University","ror":"https://ror.org/04718hx42","country_code":"TH","type":"education","lineage":["https://openalex.org/I76920116"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Narong Punnim","raw_affiliation_strings":["Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, Thailand","srinakharinwirot university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Srinakharinwirot University, Sukhumvit 23, Bangkok 10110, Thailand","institution_ids":["https://openalex.org/I76920116"]},{"raw_affiliation_string":"srinakharinwirot university","institution_ids":["https://openalex.org/I76920116"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.0812,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80789688,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9976000189781189,"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/T11130","display_name":"Coding theory and cryptography","score":0.9890999794006348,"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/mathematics","display_name":"Mathematics","score":0.8749902248382568},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.712263286113739},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6556168794631958},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6233997344970703},{"id":"https://openalex.org/keywords/block-size","display_name":"Block size","score":0.5121526718139648},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.38062989711761475},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35384196043014526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06382369995117188},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04094800353050232}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8749902248382568},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.712263286113739},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6556168794631958},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6233997344970703},{"id":"https://openalex.org/C41431624","wikidata":"https://www.wikidata.org/wiki/Q1053357","display_name":"Block size","level":3,"score":0.5121526718139648},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.38062989711761475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35384196043014526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06382369995117188},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04094800353050232},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2011/148580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/148580","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/148580.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:7f1ba705cf5345c9be501d53713424d0","is_oa":false,"landing_page_url":"https://doaj.org/article/7f1ba705cf5345c9be501d53713424d0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/148580","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/148580","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/148580.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2127319721.pdf","grobid_xml":"https://content.openalex.org/works/W2127319721.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1534899308","https://openalex.org/W2014311315","https://openalex.org/W2025231306","https://openalex.org/W2036881623","https://openalex.org/W2112641412","https://openalex.org/W2612363351","https://openalex.org/W2948461830","https://openalex.org/W4205545339","https://openalex.org/W4249181867"],"related_works":["https://openalex.org/W2077189200","https://openalex.org/W2393136772","https://openalex.org/W768788828","https://openalex.org/W4386229429","https://openalex.org/W2035025044","https://openalex.org/W3016449295","https://openalex.org/W53339341","https://openalex.org/W2484416673","https://openalex.org/W2618349488","https://openalex.org/W4362564423"],"abstract_inverted_index":{"The":[0],"original":[1],"classiffcation":[2],"of":[3,52,60],"PBIBDs":[4],"defined":[5],"group":[6,54],"divisible":[7,55],"designs":[8,56],"GDD(":[9],"v":[10,12,15,20],"=":[11,70],"1":[13,28,35],"+":[14,17,19],"2":[16,31,69],"\u22ef":[18],"g":[21,23],",":[22,24,26,29],"k":[25],"\u03bb":[27,30,34,68],")":[32],"with":[33,57,67],"\u2260":[36],"0.":[37],"In":[38],"this":[39],"paper,":[40],"we":[41],"prove":[42],"that":[43],"the":[44,50,53],"necessary":[45],"conditions":[46],"are":[47],"suffcient":[48],"for":[49],"existence":[51],"two":[58],"groups":[59],"unequal":[61],"sizes":[62],"and":[63],"block":[64],"size":[65],"three":[66],"1.":[71]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
