{"docId":6186,"paperId":5706,"url":"https:\/\/dmtcs.episciences.org\/5706","doi":"10.23638\/DMTCS-22-1-5","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":372,"name":"vol. 22 no. 1"}],"section":[{"sid":6,"title":"Combinatorics","description":[]}],"repositoryName":"arXiv","repositoryIdentifier":"1908.06679","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/1908.06679v2","dateSubmitted":"2019-08-23 19:54:09","dateAccepted":"2020-03-16 10:14:46","datePublished":"2020-03-16 10:15:00","titles":["The 3-way flower intersection problem for Steiner triple systems"],"authors":["Amjadi, H.","Soltankhah, N."],"abstracts":["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}.","Comment: 14 pages"],"keywords":["Mathematics - Combinatorics","05B05"]}