eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2020-03-16
vol. 22 no. 1
Combinatorics
10.23638/DMTCS-22-1-5
5706
journal article
The 3-way flower intersection problem for Steiner triple systems
H. Amjadi
N. Soltankhah
The flower at a point x in a Steiner triple system (X; B) is the set of all
triples containing x. Denote by J3F(r) the set of all integers k such that
there exists a collection of three STS(2r+1) mutually intersecting in the same
set of k + r triples, r of them being the triples of a common flower.
In this article we determine the set J3F(r) for any positive integer r = 0, 1
(mod 3) (only some cases are left undecided for r = 6, 7, 9, 24), and establish
that J3F(r) = I3F(r) for r = 0, 1 (mod 3) where I3F(r) = {0, 1,...,
2r(r-1)/3-8, 2r(r-1)/3-6, 2r(r-1)/3}.
https://dmtcs.episciences.org/5706/pdf
Mathematics - Combinatorics
05B05