## Abstract A wellβknown, and unresolved, conjecture states that every partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order Ο for all Ο ββ‘ 1 or 3, (mod 6), Ο ββ₯β2uβ+β1. However, some partial Steiner triple systems of order __u__ can be embedded in Steiner t
A partial Steiner triple system of order n can be embedded in a Steiner triple system of order 6n + 3
β Scribed by Charles C Lindner
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 164 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0097-3165
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π SIMILAR VOLUMES
## Phelps 2.1 will produce such a collection for each n -1/> 1. Choose U as in (3.1) above, then B,, =pBn-1 U U is a set of representatives for a CSTS(p"). Since every multiplier m =-1 (modp n'l) is an automorphism of this system f(x)=p"-lx2 +x will be an isomorphism from B,, to another CSTS(p~),
## Abstract Lindner's conjecture that any partial Steiner triple system of order __u__ can be embedded in a Steiner triple system of order __v__ if $v\equiv 1,3 \; ({\rm mod}\; 6)$ and $v\geq 2u+1$ is proved. Β© 2008 Wiley Periodicals, Inc. J Combin Designs 17: 63β89, 2009
A generalization of Cruse's Theorem on embedding partial idempotent commutative latin squares is developed and used to show that a partial m = (2k + I)-cycle system of order n can be embedded in an m-cycle system of order tm for every odd t 2 (2n + 1).
A formula is found for the total number of distinct Steiner triple systems on 2 n &1 points whose 2-rank is one higher than the possible minimum 2 n &n&1. The formula can be used for deriving bounds on the number of pairwise nonisomorphic systems for large n, and for the classification of all noniso
## Abstract The codewords at distance three from a particular codeword of a perfect binary oneβerrorβcorrecting code (of length 2^m^β1) form a Steiner triple system. It is a longstanding open problem whether every Steiner triple system of order 2^m^β1 occurs in a perfect code. It turns out that thi