In this article, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5 and type h n , namely, n β₯ 5 and n(n -1)h 2 β‘ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous
On the existence of incomplete transversal designs with block size five
β Scribed by B. Du
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 611 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We consider sets of incomplete transversal designs with block size five TD [S; u] -TD [S; n]. We show that designs exist if and only if u 2 4n, with the possible exception of 108 values of (v, n) for which existence is undecided.
π SIMILAR VOLUMES
In this article, we construct directed group divisible designs (DGDDs) with block size five, group-type h n , and index unity. The necessary conditions for the existence of such a DGDD are n β₯ 5, (n -1)h β‘ 0 (mod 2) and n(n -1)h 2 β‘ 0 (mod 10). It is shown that these necessary conditions are also su
## Abstract Let __v,k__, and __n__ be positive integers. An incomplete perfect Mendelsohn design, denoted by __k__βIPMD__(v,n)__, is a triple (__X, Y__, πΉ) where __X__ is a __v__βset (of points), __Y__ is an __n__βsubset of __X__, and πΉ is a collection of cyclically ordered __k__βsubsets of __X__ (
## Abstract Let __v__, __k__, and __n__ be positive integers. An incomplete perfect Mendelsohn design, denoted by __k__βIPMD(__v__, __n__), is a triple (__X, Y__, πΉ) where __X__ is a __v__βset (of points), __Y__ is an __n__βsubset of __X__, and πΉ is a collection of cyclically ordered __k__βsubsets
The spectrum of a-resolvable block designs