Results 21 to 30 of about 14,988 (146)
Inequalities for Semiregular Group Divisible Designs
The Annals of Statistics, 1976 Let $s_{ju}$ be the number of varieties in common to the $j$th and $u$th blocks of a symmetric semiregular group divisible design. Connor (1952) and Saraf (1961) have given inequalities for $s_{ju}$. Both these inequalities lead to the same stronger inequality $\lambda_1 \leqq s_{ju} \leqq 2\lambda_2 - 1$.
openaire +2 more sources
Constructions of biangular tight frames and their relationships with equiangular tight frames
, 2017 We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular Tight Frames ...
Cahill, Jameson +3 more
core +1 more source
Some construction of group divisible designs with singer groups
Discrete Mathematics, 1991 An MDS is a \((v,k,\lambda)\)-difference set with \(v=4(k-\lambda)\); then there exist an integer \(u\) such that \(v=4u^2\). A \((m,n,k,\lambda_1,\lambda_2)\)-DDS has the property \((M)\) if \(mn=4(k-\lambda_2)\). The case \(\lambda_1=0\) is characterized.
Arasu, K.T., Pott, Alexander
openaire +1 more source
The classification of flag-transitive Steiner 3-designs
, 2004 We solve the long-standing open problem of classifying all 3-(v,k,1) designs with a flag-transitive group of automorphisms (cf. A. Delandtsheer, Geom. Dedicata 41 (1992), p. 147; and in: "Handbook of Incidence Geometry", ed. by F.
Huber, Michael
core +1 more source
New Constructions and Necessary Conditions for 4-GDDs With Block Size 5
International Journal of Mathematics and Mathematical Sciencest-v,k,Λ designs are well-known objects of study. Here, we define t-group divisible designs (t-GDDs) and specifically study t-GDDs, where the number of groups are less than the block size. After a short survey of t-GDDs, we will present some examples of 4-
Dinkayehu M. Woldemariam, D. G. Sarvate
doaj +1 more source
Strongly regular graphs and group divisible designs [PDF]
Pacific Journal of Mathematics, 1974 0. Introduction. In the present paper, we use the counting techniques of the author's earlier work [5] to prove the converse of a result of R.C. Bose and S.S. Shrikhande [3] on geometric and pseudo-geometric graphs (q + l,q+H). Section 1 is devoted to preliminaries on strongly regular graphs and group divisible designs. We also give a brief description
openaire +3 more sources
A Generalization of Group Divisible Designs
The Annals of Mathematical Statistics, 1960 Roy [8] extended the idea of Group Divisible designs of Bose and Connor [1] to $m$-associate classes, calling such designs Hierarchical Group Divisible designs with $m$-associate classes. Subsequently, no literature is found in this direction. The purpose of this paper is to study these designs systematically.
openaire +3 more sources
FURTHER CONSTRUCTIONS OF NESTED GROUP DIVISIBLE DESIGNS
JOURNAL OF THE JAPAN STATISTICAL SOCIETY, 1996 Summary: Some methods of construction for nested group divisible designs are given. Cyclic nested group divisible designs are further discussed. Some individual plans are also tabulated with 4 new \(E\)-optimal designs.
Miao, Ying +2 more
openaire +3 more sources
Maximal determinants and saturated D-optimal designs of orders 19 and 37 [PDF]
, 2011 A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal.
Brent, Richard P. +3 more
core +1 more source
Combinatorial aspects of covering arrays
Le Matematiche, 2004 Covering arrays generalize orthogonal arrays by requiring that t -tuples be covered, but not requiring that the appearance of t -tuples be balanced.Their uses in screening experiments has found application in software testing, hardware testing, and a ...
Charles J. Colbourn
doaj