𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On balanced complementation for regular t-wise balanced designs

✍ Scribed by R. Fuji-Hara; S. Kuriki; M. Jimbo

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
610 KB
Volume
76
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Vanstone has shown a procedure, called r-com?!ementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r-complementation, called balanced complementation.

Necessary and sufficient conditions for balanced complementation which gives a regular t-wise balanced design from an existing regular t-wise balanced design are shown. We characterize those aspects of designs which permit balanced complementation.

Results obtained here will be applied to construct regular t-wise balanced designs which are useful in Statistics.

πŸ“œ SIMILAR VOLUMES

Bounding graphical t-wise balanced desig
Bounding graphical t-wise balanced designs
✍ Leo G. Chouinard II πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 167 KB

Let X be the edges of the complete graph K, on n vertices, provided with the natural action of S,, the automorphism group of K,. A t-wise balanced design (X,.8) with parameters t-((~), K, )J is said to be 9raphical if.~ is fixed under the action of S,. We show that for any pair (t, 2) with t > 1 or

A hole-size bound for incomplete t-wise
A hole-size bound for incomplete t-wise balanced designs
✍ Donald L. Kreher; Rolf S. Rees πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 140 KB

## Abstract An incomplete __t__‐wise balanced design of index Ξ» is a triple (__X,H__,ℬ︁) where __X__ is a υ–element set, __H__ is a subset of __X__ called the hole, and __B__ is a collection of subsets of __X__ called blocks, such that, every __t__‐element subset of __X__ is either in __H__ or in e

The bigraphical t-wise balanced designs
The bigraphical t-wise balanced designs of index 1
✍ Dean G. Hoffman; Donald L. Kreher πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 367 KB

## Abstract The __t__‐wise balanced designs of index 1 whose point set are the edges of __K__~__m,n__~, the complete bipartite graph, and that have the subgroup of all automorphisms that fix the two independent sets of __K~m,n~__ as an automorphism group are studied. All such designs are found. Β© 1

The bigraphical t-wise balanced designs
The bigraphical t-wise balanced designs of index two
✍ Lisa M. Weiss; Donald L. Kreher πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 998 KB

In this article we study the group S, X S, acting on the mn ordered pairs and classify all t-wise balanced designs of index 2 that have such an automorphism group. o 1995 John Wiley & Sons, Inc. ## 1. Introduction A t-wise balanced design (tBD) of type t -( v , K , A ) is a pair ( X , 3 ) where X

On Steiner 3-wise balanced designs of or
On Steiner 3-wise balanced designs of order 17
✍ E. S. Kramer; D. L. Kreher; Rudolf Mathon πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 231 KB

We determine all S(3, K, 17)'s which either; (i) have a block of size at least 6; or (ii) have an automorphism group order divisible by 17, 5, or 3; or (iii) contain a semi-biplane; or (iv) come from an S(3, K, 16) which is not an S(3, 4, 16). There is an S(3, K, 17) with |G| = n if and only if n ∈