{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:33:55Z","timestamp":1753886035782,"version":"3.41.2"},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,7,27]],"date-time":"2011-07-27T00:00:00Z","timestamp":1311724800000},"content-version":"vor","delay-in-days":207,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The original classiffcation of PBIBDs defined group divisible designs GDD(<jats:italic>v<\/jats:italic> = <jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub> + <jats:italic>v<\/jats:italic><jats:sub>2<\/jats:sub> + \u22ef + <jats:italic>v<\/jats:italic><jats:sub><jats:italic>g<\/jats:italic><\/jats:sub>, <jats:italic>g<\/jats:italic>, <jats:italic>k<\/jats:italic>, <jats:italic>\u03bb<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>\u03bb<\/jats:italic><jats:sub>2<\/jats:sub>) with <jats:italic>\u03bb<\/jats:italic><jats:sub>1<\/jats:sub> \u2260 0. In this paper, we prove that the necessary\nconditions are suffcient for the existence of the group divisible designs with two groups\nof unequal sizes and block size three with <jats:italic>\u03bb<\/jats:italic><jats:sub>2<\/jats:sub> = 1.<\/jats:p>","DOI":"10.1155\/2011\/148580","type":"journal-article","created":{"date-parts":[[2011,7,27]],"date-time":"2011-07-27T19:00:20Z","timestamp":1311793220000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Group Divisible Designs with Two Associate Classes and <i>\u03bb<\/i><sub>2<\/sub> = 1"],"prefix":"10.1155","volume":"2011","author":[{"given":"Nittiya","family":"Pabhapote","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Narong","family":"Punnim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,7,27]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1998.2868"},{"key":"e_1_2_5_2_2","first-page":"33","article-title":"The existence of group divisible designs with first and second associates, having block size 3","volume":"54","author":"Fu H. L.","year":"2000","journal-title":"Ars Combinatoria"},{"volume-title":"Design Theory","year":"1997","author":"Lindner C. C.","key":"e_1_2_5_3_2"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00373\u2010010\u20100951\u20108"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2280741"},{"volume-title":"Handbook of Combinatorial Designs","year":"2007","author":"Colbourn C. J.","key":"e_1_2_5_6_2"},{"key":"e_1_2_5_7_2","unstructured":"ChaiyasenaA. HurdS. P. PunnimN. andSarvateD. G. Group divisible designs with two associattion classes Journal of Combinatorial Mathematics and Combinatorial Computing. In press."}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/148580.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/148580.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/148580","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T13:46:04Z","timestamp":1718027164000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/148580"}},"subtitle":[],"editor":[{"given":"Michael","family":"Tom","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/148580"],"URL":"https:\/\/doi.org\/10.1155\/2011\/148580","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2011-01-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-05-19","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-07-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"148580"}}