Symmetry of a group divisible design with r=λ1+1

2002 ◽  
Vol 106 (1-2) ◽  
pp. 31-37
Author(s):  
Tsutomu Shimata ◽  
Sanpei Kageyama
Keyword(s):  
Group Divisible Design ◽  
Divisible Design ◽  
Group Divisible

OCDs in Group Divisible Design Set-Up

2015 ◽  
pp. 65-88
Author(s):  
Premadhis Das ◽  
Ganesh Dutta ◽  
Nripes Kumar Mandal ◽  
Bikas Kumar Sinha
Keyword(s):  
Group Divisible Design ◽  
Divisible Design ◽  
Group Divisible ◽  
Set Up

On Automorphism Groups of Divisible Designs

1982 ◽  
Vol 34 (2) ◽  
pp. 257-297 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Difference Sets ◽  
Difference Set ◽  
Relative Difference ◽  
Block Designs ◽  
Divisible Design ◽  
Finite Projective Spaces ◽  
Group Divisible ◽  
Singer Group

A (group) divisible design is a tactical configuration for which the v points are split into m classes of n each, such that points have joining number λ (resp. λ2) if and only if they are in the same (resp. in different) classes. We are interested in such designs with a nice automorphism group. We first investigate divisible designs with equally many points and blocks admitting an automorphism group acting regularly on all points and on all blocks, i.e., with a Singer group (Singer [50] obtained the first result in this direction for the finite projective spaces).As in the case of block designs, one may expect a divisible design with a Singer group to be equivalent to some sort of difference set; as it turns out, one here obtains a generalisation of the relative difference sets of Butson and Elliott [11] and [20].

Characterization of Group Divisible Designs

2016 ◽  
Vol 4 (2) ◽  
pp. 161-175
Author(s):  
Jyoti Sharma ◽  
Jagdish Prasad ◽  
D. K. Ghosh
Keyword(s):  
Group Divisible Designs ◽  
Group Divisible

Further Results on GGD Designs

1982 ◽  
Vol 31 (1-2) ◽  
pp. 53-62
Author(s):  
Sanjeev C. Panandikar
Keyword(s):  
New Methods ◽  
Characteristic Roots ◽  
Group Divisible ◽  
The Matrix

In this paper we discuss some of the properties of the matrix ( NN') of the Generalised Group Divisible (GGD) design with λ ij ; i, j=l,2. The properties are the characteristic roots, the Hasse­Minkowski invariant and the nonexistence theorems. Some new methods for constructing GGD designs are also given.

On the construction of group divisible incomplete block designs

1975 ◽  
Vol 3 (2) ◽  
pp. 285-288
Author(s):  
H. T. Trivedi ◽  
V. K. Sharma
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Group Divisible
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