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Embeddings of resolvable group divisible designs with block size 3

Jun Shen, Hao Shen
2006 Designs, Codes and Cryptography  
The necessary conditions for the existence of a (2 × 4, λ)-splitting GDD of type It is proved in this paper that these conditions are also sufficient except for λ ≡ 0 (mod 16) and (g, v) = (3, 3).  ...  In the recursive constructions of splitting BIBDs, splitting group divisible designs (splitting GDDs) play an important role.  ...  A transversal design, denoted by TD λ (k, m), is a triple (V, G, B), where 1) V is a set of km elements (called points); 2) G is a partition of V into k subsets (called groups), each of size m; 3) B is  ... 
doi:10.1007/s10623-006-9010-0 fatcat:frheywungfcg5emrfhmbs5ku24

Page 1704 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Kelly (1-MIS) 88d:05025 05B05 Rees, Rolf (3-WTRL-B); Stinsun, D. R. (3-MB-C) On resolvable group-divisible designs with block size 3. Ars Combin. 23 (1987), 107-120.  ...  A > 1 and block size k into a design with at most {(3*~'An?)  ... 

Page 38 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
We also give an infinite series of resolvable group divisible designs with block size 4 and group size 2, in which the smallest one is of order 32; this is the first example of an RGD(4, 2; v).” 98a:05023  ...  {For the entire collection see MR 97i:05004. } Paul-Hermann Zieschang (D-KIEL; Kiel) 98a:05022 05B05 Shen, Hao (PRC-JTU-AM; Shanghai) Existence of resolvable group divisible designs with block size four  ... 

Page 4457 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
This paper deals with group divisible designs, GDD(n, m; 3; A), A2), of block size 3 where the vertex set is partitioned into m sets (called groups) of size n, in which each pair of vertices occur in A  ...  In this paper, the spectrum of orthogonal 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.  ... 

On combinatorial designs with subdesigns

Rolf Rees, D.R. Stinson
1989 Discrete Mathematics  
We develop some powerful techniques by which (certain classes of) combinatorial designs with pre-specified subdesigns can be constructed.  ...  The spectrum of these designs was determined by Stinson [32]:  ...  A new class of group-divisible designs with block size 4 In this section we will construct our group-divisible designs, using as our primary tool the following construction. Proof.  ... 
doi:10.1016/0012-365x(89)90365-8 fatcat:fnyn6cyzhjff5fpajz3eqvu2ji

Page 2336 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Summary: “Large sets of disjoint group-divisible designs with block size three and type 2"4!' have been studied by Schellenberg, Chen, Lindner and Stinson.  ...  [Zhu, Lie] (PRC-SOO; Suzhou) Large sets of disjoint group-divisible designs with block size three and type 2”4'. (English summary) J. Combin. Des. 9 (2001), no. 4, 285-296.  ... 

Page 2459 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
A group divisible (GD) design with parameters vy = nm,n,k,r,A,,A2 is an arrangement of v treatments in b blocks in such a way that each block is of size k (< v), each treatment appears r times; and the  ...  The constructions are based on the existence of some group-divisible designs, frames, etc. Constructions of such designs with small parameters are also obtained.  ... 

Page 4384 of Mathematical Reviews Vol. , Issue 81K [page]

1981 Mathematical Reviews  
B(v,k,A) denotes a balanced incomplete block design on v ele- ments with block size k and each pair in A blocks, and RB(v, k,A) denotes a resolvable such design.  ...  Families of Hadamard group divisible designs. J. Statist. Plann. Inference 3 (1979), no. 4, 387—394 (1980).  ... 

Page 2993 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
“The most widely studied classes of block designs are triple systems; that is, block designs with block size 3. It is well known that nontrivial triple systems cannot have a blocking set.  ...  order nm with block size 4 admitting a blocking set for every n = 1 (mod 3) (except possibly n = 19,34,37,46 and 58).  ... 

Page 1287 of Mathematical Reviews Vol. , Issue 91C [page]

1991 Mathematical Reviews  
Let S = (P,B) (P = “points”; B = “blocks”) satisfy each of the following: (1) All points are of size r. (2) All blocks have size r— Ac, Ac <r. (3) Two distinct points are incident with either 0 or A common  ...  (IR-ISFA) Embedding of quasi-residual divisible semi-symmetric designs with parameters (r,/,c). J. Statist. Plann. Inference 24 (1990), no. 1, 55-67.  ... 

Page 7168 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
The construction uses Steiner systems and known results concerning {3}-group divisible designs. William I.  ...  Summary: “It is shown that a resolvable BIBD with block size five and index two exists whenever v = 5 (mod 10) and v > 50722 395.  ... 

Constructions and uses of incomplete pairwise balanced designs [article]

Peter J. Dukes, Esther R. Lamken
2018 arXiv   pre-print
As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs.  ...  We give explicit constructions for incomplete pairwise balanced designs IPBD((v;w),K), or, equivalently, edge-decompositions of a difference of two cliques K_v ∖ K_w into cliques whose sizes belong to  ...  We begin by citing a known existence result for resolvable group divisible designs having fixed group size and a single block size. Theorem 3.1 ([4]).  ... 
arXiv:1809.07866v1 fatcat:yqvrg5kzvveh5fzkuir2boa5ie

Page 5739 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
The authors also give a few more results for other values of 2. Here they discuss the BRDs with block size 5. R. N.  ...  Dedicata 16 (1984), no. 2, 167-178; MR 851:05060] proved an exponential lower bound on the number of non-isomorphic affine resolvable designs with these parameters for d > 3.  ... 

Page 3005 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
A restricted resolvable design RRP(p,k) is a pairwise balanced design on p points, with blocks of size 2 and 3, such that the blocks can be partitioned into k resolution classes, each of which partitions  ...  divisible designs.  ... 

Page 5348 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
Discrete Math. 92 (1991), no. 1-3, 137-144. The authors discuss the construction of group divisible partially balanced bipartite block (GD PBB) designs.  ...  Furthermore, we determine the parameters of regular group divisible designs with 42 = A; — 1 such that rk — Av is at most 11 and further equal to 13, 17, 19.  ... 
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