Amjadi, H. and Soltankhah, N. - The 3-way flower intersection problem for Steiner triple systems

dmtcs:5706 - Discrete Mathematics & Theoretical Computer Science, March 16, 2020, vol. 22 no. 1 - https://doi.org/10.23638/DMTCS-22-1-5
The 3-way flower intersection problem for Steiner triple systems

Authors: Amjadi, H. and Soltankhah, N.

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}.


Volume: vol. 22 no. 1
Section: Combinatorics
Published on: March 16, 2020
Submitted on: August 23, 2019
Keywords: Mathematics - Combinatorics,05B05


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