The existence of FGDRP\((3,g^{u})\)'s
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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 $(g,u)\in \{(6,15),(9,18),(9,28),(9,34),(30,15)\}$.
@article{10_37236_123,
author = {Jie Yan and Chengmin Wang},
title = {The existence of {FGDRP\((3,g^{u})\)'s}},
journal = {The electronic journal of combinatorics},
year = {2009},
volume = {16},
number = {1},
doi = {10.37236/123},
zbl = {1178.05020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/123/}
}
Jie Yan; Chengmin Wang. The existence of FGDRP\((3,g^{u})\)'s. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/123
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