𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A partial Steiner triple system of order n can be embedded in a Steiner triple system of order 6n + 3

✍ Scribed by Charles C Lindner


Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
164 KB
Volume
18
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


A conjecture on small embeddings of part
✍ Darryn Bryant πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 106 KB πŸ‘ 1 views

## Abstract A well‐known, 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 υ ≑ 1 or 3, (mod 6), υ β‰₯ 2u + 1. However, some partial Steiner triple systems of order __u__ can be embedded in Steiner t

A construction of cyclic Steiner triple
✍ K.T Phelps πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 230 KB

## 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~),

A proof of Lindner's conjecture on embed
✍ Darryn Bryant; Daniel Horsley πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 243 KB πŸ‘ 1 views

## 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: 63–89, 2009

A partial m=(2k+1)-cycle system of order
✍ C.C. Lindner; C.A. Rodger πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 566 KB

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 Mass Formula for Steiner Triple System
✍ Vladimir D. Tonchev πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 116 KB

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

There exist Steiner triple systems of or
✍ Patric R. J. Γ–stergΓ₯rd; Olli Pottonen πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 74 KB πŸ‘ 1 views

## Abstract The codewords at distance three from a particular codeword of a perfect binary one‐error‐correcting code (of length 2^m^βˆ’1) form a Steiner triple system. It is a longstanding open problem whether every Steiner triple system of order 2^m^βˆ’1 occurs in a perfect code. It turns out that thi