In 1963, Shrikhande and Raghavarao [5] published a recursive construction for designs that starts with a resolvable design (the “master design”) and then uses a second design (“the indexing design”) to take certain unions of blocks in each parallel class of the master design. Several variations of this construction have been studied by different authors. We revisit this construction, concentrat...

We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v, 3, λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v, 3, λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if...

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].

In a t-(v, k, λ) directed design the blocks are ordered k-tuples and every ordered t-tuple of distinct points occurs in exactly λ blocks (as a subsequence). We study t-(v, 5, 1) directed designs with t = 3 and t = 4. In particular, we construct the first known examples, and an infinite class, of 3-(v, 5, 1) directed designs, and the first known infinite class of 4-(v, 5, 1) directed designs.

In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type gu and show that such a design exists if and only if u ≥ 4, g(u − 2) ≥ 10, g(u − 1) ≡ 0 (mod 3) and u(u− 1)g2 ≡ 0 (mod 12). © 2009 Elsevier B.V. All rights reserved.

We study three similar bijections on set partitions. The first is an involution defined by Kasraoui and Zeng which proves the symmetry of the distribution of crossings and nestings. We show that a stronger result can be deduced. The second gives a bijective proof of the equivalence of two statistics with a q-Stirling distribution. The third proves the equivalence of a multivariate block size di...

We propose a new indexing scheme, called the CRB-tree, for efficiently answering range-aggregate queries. The range-aggregate problem is defined as follows: Given a set of weighted points in R, compute the aggregate of weights of points that lie inside a d-dimensional query rectangle. In this paper we focus on range-COUNT, SUM, AVG aggregates. First, we develop an indexing scheme for answering ...

For each admissible v, we exhibit a path design P (v, 4, 1) with a spanning set of minimum cardinality and a P (v, 4, 1) with a scattering set of maximum

In this paper, we remove the outstanding values m for which the existence of a GBTD(4,m) has not been decided previously. This leads to a complete solution to the existence problem regarding GBTD(4,m)s.

The existence of (M, B)-optimal designs for block size three is completely settled. Such a design is a collection of b triples on v elements so that for every two elements the numbers of triples containing them differ by at most one, and for every two pairs of elements the numbers of triples containing them also differ by at most one.