Results 1 - 10 of 184

Existence of resolvable group divisible designs with block size four I

by Hao Shen , Jiaying Shen , 2002
"... ..."
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Modified group divisible designs with block size 4

by Ahmed M. Assaf
"... 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

by Alan C. H. Ling, Charles J. Colbourn - 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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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

by Peter Danziger, Chengmin Wang - 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

by Charles J. Colbourn, Charles J. Colbourn, Peter B. Gibbons, Peter B. Gibbons - 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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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

by Peter Danziger, Brett Stevens - 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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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

by Zhike Jiang - 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

by Jun Shen - 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

by Rolf S. Rees, Douglas R. Stinson - 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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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

by J. Yin, J. Wang
"... 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 of 184