Steiner triple systems and spreading sets in projective spaces
Combinatorics
2021-03-02 v1
Abstract
We address several extremal problems concerning the spreading property of point sets of Steiner triple systems. This property is closely related to the structure of subsystems, as a set is spreading if and only if there is no proper subsystem which contains it. We give sharp upper bounds on the size of a minimal spreading set in a Steiner triple system and show that if all the minimal spreading sets are large then the examined triple system must be a projective space. We also show that the size of a minimal spreading set is not an invariant of a Steiner triple system.
Cite
@article{arxiv.2103.00922,
title = {Steiner triple systems and spreading sets in projective spaces},
author = {Zoltán Lóránt Nagy and Levente Szemerédi},
journal= {arXiv preprint arXiv:2103.00922},
year = {2021}
}