The 3-way flower intersection problem for Steiner triple systems
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1
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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}.
@article{DMTCS_2020_22_1_a8,
author = {Amjadi, H. and Soltankhah, N.},
title = {The 3-way flower intersection problem for {Steiner} triple systems},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {2020-2021},
doi = {10.23638/DMTCS-22-1-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-5/}
}
TY - JOUR AU - Amjadi, H. AU - Soltankhah, N. TI - The 3-way flower intersection problem for Steiner triple systems JO - Discrete mathematics & theoretical computer science PY - 2020-2021 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-5/ DO - 10.23638/DMTCS-22-1-5 LA - en ID - DMTCS_2020_22_1_a8 ER -
%0 Journal Article %A Amjadi, H. %A Soltankhah, N. %T The 3-way flower intersection problem for Steiner triple systems %J Discrete mathematics & theoretical computer science %D 2020-2021 %V 22 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-5/ %R 10.23638/DMTCS-22-1-5 %G en %F DMTCS_2020_22_1_a8
Amjadi, H.; Soltankhah, N. The 3-way flower intersection problem for Steiner triple systems. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1. doi: 10.23638/DMTCS-22-1-5
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