episciences.org_5706_1675649385 1675649385 episciences.org raphael.tournoy+crossrefapi@ccsd.cnrs.fr episciences.org Discrete Mathematics & Theoretical Computer Science 1365-8050 03 16 2020 vol. 22 no. 1 Combinatorics 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}. 03 16 2020 5706 https://arxiv.org/licenses/nonexclusive-distrib/1.0 arXiv:1908.06679 10.48550/arXiv.1908.06679 https://arxiv.org/abs/1908.06679v1 10.23638/DMTCS-22-1-5 https://dmtcs.episciences.org/5706 https://dmtcs.episciences.org/6186/pdf https://dmtcs.episciences.org/6186/pdf