Extensions of Steiner Triple Systems
Combinatorics
2025-01-09 v2
Abstract
In this article we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a powerful method for constructing Steiner triple systems containing Veblen points.
Cite
@article{arxiv.2406.12796,
title = {Extensions of Steiner Triple Systems},
author = {Giovanni Falcone and Agota Figula and Mario Galici},
journal= {arXiv preprint arXiv:2406.12796},
year = {2025}
}