Modified group divisible designs with block size 4 and λ>1
نویسنده
چکیده
It is shown here that the necessary conditions for the existence of MGD[4, A m, n] for A ~ 2 are sufficient with the exception of MGO(4, 3, 6,23].
منابع مشابه
Splitting group divisible designs with block size 2×4
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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The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.
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A resolvable modified group divisible design (RMGD) is a modified group divisible design whose blocks can be partitioned into parallel classes. We show that the necessary conditions for the existence of a 3-RMGDDλ of type g, namely g ≥ 3, u ≥ 3, gu ≡ 0 mod 3 and λ(g−1)(u−1) ≡ 0 mod 2, are sufficient with the two exceptions of (g, u, λ) ∈ {(6, 3, 1), (3, 6, 1)}.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 16 شماره
صفحات -
تاریخ انتشار 1997