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184
Modified group divisible designs with block size 4
"... Abstract: 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]. 1. ..."
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Abstract: 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]. 1.
Modified Group Divisible Designs With Block Size Four
- Discrete Math
, 1998
"... The existence of modified group divisible designs with block size four is settled with a handful of possible exceptions. 1 Introduction A group divisible design (GDD) is a triple (X; G; B) which satisfies the following properties: (1) G is a partition of a set X (of points) into subsets called grou ..."
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Cited by 2 (0 self)
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The existence of modified group divisible designs with block size four is settled with a handful of possible exceptions. 1 Introduction A group divisible design (GDD) is a triple (X; G; B) which satisfies the following properties: (1) G is a partition of a set X (of points) into subsets called
Resolvable modified group divisible designs with higher index
- AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 41 (2008), PAGES 37–44
, 2008
"... 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 u, namely g ≥ 3, u ≥ 3, gu ≡ 0 mod 3 and λ(g −1)(u−1) ≡ 0 mod 2, are suffic ..."
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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 u, namely g ≥ 3, u ≥ 3, gu ≡ 0 mod 3 and λ(g −1)(u−1) ≡ 0 mod 2
Uniform Orthogonal Group Divisible Designs with Block Size Three
- J. Math
, 1996
"... The spectrum of orthogonal group divisible designs with block size three, and u groups each of size g, is studied. Existence is settled with few possible exceptions for each group size g. 1 Definitions and Background A pairwise balanced design (orPBD)isapair(X,A) such that X is a set of elements ca ..."
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Cited by 2 (1 self)
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The spectrum of orthogonal group divisible designs with block size three, and u groups each of size g, is studied. Existence is settled with few possible exceptions for each group size g. 1 Definitions and Background A pairwise balanced design (orPBD)isapair(X,A) such that X is a set of elements
Class-Uniformly Resolvable Group Divisible Structures II: Frames
- Electron. J. Combin
, 2004
"... We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions, including extremal bounds, build the foundation for general CURF constructions, including a frame varia ..."
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Cited by 3 (1 self)
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We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions, including extremal bounds, build the foundation for general CURF constructions, including a frame
Concerning cyclic group divisible designs with block size three
- Australas. J. Combin
, 1996
"... 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. 1 ..."
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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. 1
Splitting group divisible designs with block size 2 × 4
- AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 47 (2010), PAGES 197–204
, 2010
"... The necessary conditions for the existence of a (2 × 4,λ)-splitting GDD of type g v are gv ≥ 8, λg(v − 1) ≡ 0(mod4),λg 2 v(v − 1) ≡ 0(mod32). 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 necessary conditions for the existence of a (2 × 4,λ)-splitting GDD of type g v are gv ≥ 8, λg(v − 1) ≡ 0(mod4),λg 2 v(v − 1) ≡ 0(mod32). It is proved in this paper that these conditions are also sufficient except for λ ≡ 0 (mod 16) and (g, v) =(3, 3).
Frames with Block Size Four
- CANAD. J. MATH
, 1992
"... We investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs. Our main result is that a frame of type h , having blocks of size four, exists 0 mod 3 and h(u 0 mod 4, except possibly where ..."
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Cited by 11 (0 self)
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We investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs. Our main result is that a frame of type h , having blocks of size four, exists 0 mod 3 and h(u 0 mod 4, except possibly where
(3, A)-GROUP DIVISIBLE COVERING DESIGNS
"... Abstract Let U, g, k and A be positive integers with u:::: k. A (k, A)-grOUp divisible covering design ((k, A)-GDCD) with type gU is a A-cover of pairs by k-tuples of a gu-set X with u holes of size g, which are disjoint and spanning. The covering number, C(k, A; gil), is the minimum number of block ..."
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Abstract Let U, g, k and A be positive integers with u:::: k. A (k, A)-grOUp divisible covering design ((k, A)-GDCD) with type gU is a A-cover of pairs by k-tuples of a gu-set X with u holes of size g, which are disjoint and spanning. The covering number, C(k, A; gil), is the minimum number
Results 1 - 10
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184