𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the existence of incomplete transversal designs with block size five

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Existence of HPMDs with block size five
✍ F. E. Bennett; Y. Chang; J. Yin; H. Zhang πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 194 KB

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 ≑ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous

Existence of directed GDDs with block si
✍ F. E. Bennett; Nabil Shalaby; Jianxing Yin πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 393 KB πŸ‘ 1 views

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 ≑ 0 (mod 2) and n(n -1)h 2 ≑ 0 (mod 10). It is shown that these necessary conditions are also su

Incomplete perfect mendelsohn designs wi
✍ F. E. Bennett; H. Shen; J. Yin πŸ“‚ Article πŸ“… 1993 πŸ› John Wiley and Sons 🌐 English βš– 676 KB

## Abstract Let __v,k__, and __n__ be positive integers. An incomplete perfect Mendelsohn design, denoted by __k__‐IPMD__(v,n)__, is a triple (__X, Y__, 𝔹) where __X__ is a __v__‐set (of points), __Y__ is an __n__‐subset of __X__, and 𝔹 is a collection of cyclically ordered __k__‐subsets of __X__ (

Incomplete perfect mendelsohn designs wi
✍ F. E. Bennett; H. Shen; J. Yin πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 643 KB

## Abstract Let __v__, __k__, and __n__ be positive integers. An incomplete perfect Mendelsohn design, denoted by __k__‐IPMD(__v__, __n__), is a triple (__X, Y__, 𝔹) where __X__ is a __v__‐set (of points), __Y__ is an __n__‐subset of __X__, and 𝔹 is a collection of cyclically ordered __k__‐subsets