Paper Info
Title
The number of common flowers of two STS(v)s and embeddable Steiner triple trades.
Abstract
A flower, FS(x), around a point x in a Steiner triple system D=(V,B) is the set of all triples in B which contain the point x, namely FD(x)={b∈B∣x∈b}. This paper determines the possible number of common flowers that two Steiner triple systems can have in common. For all admissible pairs (k,v) where k≤v−6 we construct a pair of Steiner triple systems of order v where the flowers around k elements of V are identical in both Steiner triple systems, except for the pairs (2,9), (3,9) and (6,13). Equivalently this result shows that there is a Steiner triple trade of foundation l=v−k that can be embedded in a STS(v) for each admissible v and 6≤l≤v except when (l,v)=(6,9),(7,9) or (7,13).
Year
DOI
Venue
2013
10.1016/j.disc.2013.01.003
Discrete Mathematics
Keywords
Field
DocType
Block designs,Intersection problems,Flower intersection,Steiner triple trades,Embeddable trades
Discrete mathematics,Combinatorics,Monad (category theory),Mathematics,Steiner system
Journal
Volume
Issue
ISSN
313
7
0012-365X
Citations 
PageRank 
References 
0
0.34
3
Authors
1
Name
Order
Citations
PageRank
Emine Şule Yazıcı1257.25