{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809562,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>By an FGDRP$(3,g^u)$, we mean a uniform frame $(X,\\cal G,\\cal A)$ of block size 3, index 2 and type $g^u$, where the blocks of $\\cal{A}$ can be arranged into a $gu\/3\\times gu$ array. This array has the properties: (1) the main diagonal consists of $u$ empty subarrays of sizes $g\/3\\times g$; (2) the blocks in each column form a partial parallel class partitioning $X \\setminus G$ for some $G\\in \\cal G$, while the blocks in each row contain every element of $X \\setminus G$ $3$ times and no element of $G$ for some $G\\in \\cal{G}$. The obvious necessary conditions for the existence of an FGDRP$(3,g^u)$ are $u\\geq 5$ and $g\\equiv 0$ (mod 3). In this paper, we show that these conditions are also sufficient with the possible exceptions of $(g,u)\\in \\{(6,15),(9,18),(9,28),(9,34),(30,15)\\}$.<\/jats:p>","DOI":"10.37236\/123","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:33:07Z","timestamp":1578717187000},"source":"Crossref","is-referenced-by-count":1,"title":["The Existence of FGDRP$(3,g^u)'$s"],"prefix":"10.37236","volume":"16","author":[{"given":"Jie","family":"Yan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengmin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:05:36Z","timestamp":1579316736000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/123","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,3,13]]},"article-number":"R34"}}