## Abstract Transverse Steiner quadruple systems with five holes are either of type __g__^5^ or __g__^4^__u__^1^. We concentrate on the systems of type g^4^__u__^1^ and settle existence except when __g__ β‘ __u__ β‘ 2 (mod 4) and all except 40 parameter situations when __g__ β‘ __u__ + 2 β‘ 0 (mod 4).
Uniform room frames with five holes
β Scribed by J. H. Dinitz; E. R. Lamken
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 264 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
Abstract
In 1981, Dinitz and Stinson [2] proved that the necessary conditions were sufficient for the existence of a Room frame of type t^u^ for all u β₯ 6. Very recently, Zhu Lie and Ge Gennian [5] constructed all t^5^ Room frames except for four missing orders. In this article we construct t^5^ Room frames for t = 11,13,17, and 19; this completes the proof that the necessary conditions are sufficient for the existence of a Room frame of type t^5^. Β© 1993 John Wiley & Sons, Inc.
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