Pairwise orthogonal F-rectangle designs
โ Scribed by W.T. Federer; A.S. Hedayat; J.P. Mandeli
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 577 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let K = {k,, , k,} be a set of block sizes, and let (pr, , p,} be nonnegative numbers with Cy!',,p, = 1. We prove the following theorem: for any E >O, if a (u, K, 1) pairwise balanced design exists and v is sufficiently large, then a (u, K, 1) pairwise balanced design exists in which the fraction
for some permutation ' of the set f1Y 2Y F F F Y 2ng. An inยฎnite number of arrays which are suitable for any amicable set of eight circulant matrices are introduced. Applications include new classes of orthogonal designs.
We consider the problem of determining cp(G v KC), the smallest number of cliques required to partition the edge set of the graph G v K~, where G is a finite simple graph and K~, is the empty graph on m vertices. A lower bound on cp(G v K~,,,) is obtained which, when applied to the case G = K,, shar