Fixed block configuration group divisible designs with block size six
نویسندگان
چکیده
منابع مشابه
Group Divisible Designs With Two Groups and Block Size Five With Fixed Block Configuration
We present constructions and results about GDDs with two groups and block size five in which each block has Configuration (s, t), that is, in which each block has exactly s points from one of the two groups and t points from the other. After some results for a general k, s and t, we consider the (2, 3) case for block size 5. We give new necessary conditions for this family of GDDs and give mini...
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We give some constructions of new infinite families of group divisible designs, GDD(n, 2, 4; 1, 2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3 n 8. For n= 10 there is one missing critical design. If 1> 2, then the necessary conditions are sufficient for n ≡ 4, 5, 8 (mod 12). For each of n=10, 15, 16, 17, 18, 19, and 20 we...
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The necessary conditions for the existence of a (2 × 4, λ)-splitting GDD of type g are gv ≥ 8, λg(v−1) ≡ 0 (mod 4), λg2v(v−1) ≡ 0 (mod 32). It is proved in this paper that these conditions are also sufficient except for λ ≡ 0 (mod 16) and (g, v) = (3, 3).
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We determine a necessary and sufficient condition for the existence of a cyclic {3}-GDD with a uniform group size 6n. This provides a fundamental class of ingredients for some recursive constructions which settle existence of k-rotational Steiner triple systems completely.
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The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.11.002